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Parametriza\303\247\303\243o Trigonom\303\251trica da Elipse
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Introdu\303\247\303\243o</Font></Text-field> JSFH Um c\303\255rculo centrado na origem \303\251 facilmente parametrizado trigonometricamente como 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, onde LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 o raio do c\303\255rculo. Se o centro do c\303\255rculo \303\251 transferido para o ponto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJoRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiLEYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYlUSJrRidGNEY3Rj5GPkY+, a parametriza\303\247\303\243o trigonom\303\251trica facilmente se estende a 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. Uma elipse cuja forma padr\303\243o em coordenadas Cartesianas \303\251 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 tamb\303\251m pode ser parametrizado trigonometricamente como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSI9RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUYsNiVRImhGJ0YvRjItRkA2LVEiK0YnRj1GQ0ZGRkhGSkZMRk5GUC9GU1EsMC4yMjIyMjIyZW1GJy9GVkZobi1GLDYlUSJhRidGL0YyLUZANi1RIn5GJ0Y9RkNGRkZIRkpGTEZORlAvRlNRJjAuMGVtRicvRlZGYW8tRiw2JVEkY29zRicvRjBGRUY9RjUtRkA2LVEiLEYnRj1GQy9GR0YxRkhGSkZMRk5GUEZgby9GVlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJ5RidGL0YyRj8tRiw2JVEia0YnRi9GMkZaLUYsNiVRImJGJ0YvRjJGXW8tRiw2JVEkc2luRidGZm9GPUY1Rj0= desde que 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 No artigo deste m\303\252s, discutiremos uma parametriza\303\247\303\243o trigonom\303\251trica para a elipse cuja equa\303\247\303\243o Cartesiana cont\303\251m um LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjeHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-termo, indicando que os eixos da elipse s\303\243o transladados em rela\303\247\303\243o aos eixos de coordenadas.
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Inicializa\303\247\303\265es</Font></Text-field> JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRLkxpbmVhckFsZ2VicmFGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiOkYnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRJnBsb3RzRidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIjpGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQ= JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Parametriza\303\247\303\243o Trigonom\303\251trica de um C\303\255rculo</Font></Text-field> JSFH N\303\243o \303\251 preciso ir muito longe no curso de C\303\241lculo para encontrar a parametriza\303\247\303\243o trigonom\303\251tricas de um c\303\255rculo. Assim, o c\303\255rculo 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 JSFH \303\251 facilmente parametrizado como 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. Naturalmente, se 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, ent\303\243o o c\303\255rculo \303\251 dado simplesmente por 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. Em qualquer evento, a parametriza\303\247\303\243o trigonom\303\251trica est\303\241 livre das quest\303\265es de ramo que faz a representa\303\247\303\243o expl\303\255cita 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 o que \303\251 muito mais complicado de trabalhar.JSFH JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Parametriza\303\247\303\243o Trigonom\303\251trica S</Font>imples de uma Elipse</Text-field> JSFH A parametriza\303\247\303\243o trigonom\303\251trica de uma elipse com eixos paralelos aos eixos de coordenadas \303\251 quase t\303\243o familiar como a parametriza\303\247\303\243o trigonom\303\251trica de um c\303\255rculo. Assim, a elipse 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 JSFH \303\251 facilmente parametrizada como 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. JSFH Para obter uma parametriza\303\247\303\243o trigonom\303\251trica equivalente de uma elipse cujos eixos n\303\243o s\303\243o paralelos aos eixos de coordenadas exige a aplica\303\247\303\243o de ambos, uma transla\303\247\303\243o e uma rota\303\247\303\243o, c\303\241lculos que podem ser encontrados em um texto de geometria anal\303\255tica de n\303\255vel de faculdade. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Analisando uma Equa\303\247\303\243o Quadr\303\241tica no Maple</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Considere, ent\303\243o, a equa\303\247\303\243o quadr\303\241tica 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 cujo gr\303\241fico \303\251 visto na Figura 1. Esta figura \303\251 obtida conforme a Tabela 1, primeiro carregando o pacote Student Precalculus, ent\303\243o aplicar o Menu de Contexto para a equa\303\247\303\243o quadr\303\241tica, selecionando de Tutors\342\211\273Conic Sections. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tools\342\211\273Load Package: Student Precalculus with(Student:-Calculus1): Carregar Student:-Precalculus with(Student:-Precalculus):
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Figura 1 Tutor de Se\303\247\303\265es C\303\264nicas aplicado \303\240 equa\303\247\303\243o quadr\303\241tica 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
Tabela 1 Aplica\303\247\303\243o do Tutor de Se\303\247\303\265es C\303\264nicas para 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 . A op\303\247\303\243o "Constrained Scaling" foi selecionada na caixa de di\303\241logo Plot Options. A forma padr\303\243o \303\251 exibida no LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictRiw2JVEieUYnRi9GMkY1Rjk=-plano cujos eixos de coordenadas s\303\243o alinhados com os eixos da elipse. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Figura 2 mostra todos os dados fornecidos pelo Tutor de Se\303\247\303\265es C\303\264nicas. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= classe: elipse excentricidade: .884 Semieixo maior (a): 11.5 Semieixo menor (b): 5.37 latus rectum: 5.03 \303\242nglo: .448 ----------------------------- No xy-plano: v\303\251rtices: [(.573e-1,-2.90), (20.7,7.03)] focos: [(1.26,-2.32), (19.5,6.46)] centro (h,k): (10.4,2.07) diretriz: y = -2.08*x+53.6 ----------------------------- No x'y'-plano: v\303\251rtices: [(-1.20,-2.64), (21.7,-2.64)] focos: [(.131,-2.64), (20.4,-2.64)] centro (h',k'): (10.3,-2.64) diretriz: x' = 23.2 Figura 2 Dados fornecidos pelo Tutor de Se\303\247\303\265es C\303\264nicas
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Maple declara que a quadr\303\241tica define uma elipse, e d\303\241 seus par\303\242metros no LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjeHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-plano original e no LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictRiw2JVEieUYnRi9GMkY1Rjk=-plano onde os eixos de coordenadas est\303\243o alinhados com os eixos da elipse. Al\303\251m da excentricidade, os focos e os v\303\251rtices s\303\243o dados em ambos os planos, a equa\303\247\303\243o da diretriz \303\251 dada no LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZwcmltZTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictRiw2JVEieUYnRi9GMkY1Rjk=-plano e o deslocamento angular entre os dois conjuntos de eixos \303\251 fornecido. Infelizmente, o Tutor n\303\243o tem espa\303\247o suficiente para mostrar a forma exata de qualquer uma destas quantidades, que pode ser grande e pesado. Assim, os dados s\303\243o relatados em forma de ponto flutuante com um n\303\272mero abreviado de d\303\255gitos. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tabela 2 mostra uma an\303\241lise alternativa da elipse, esta fornecida pelo pacote geometry. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= O pacote geometry tem que ser carregado com a sintaxe mostrada \303\240 direita. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRKWdlb21ldHJ5RidGL0YyL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIjpGJ0Y9LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQ= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder A elipse \303\251 mostrada ao pacote com a sintaxe mostrada \303\240 direita. A elipse \303\251 chamada de "E" por este comando. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoZWxsaXBzZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzY/LUYsNiVRIkVGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUkjbW5HRiQ2JFEiM0YnRkEtRj42LVEifkYnRkFGQy9GR0ZFRkhGSkZMRk5GUEZSL0ZWRlQtSSVtc3VwR0YkNiUtRiw2JVEieEYnRi9GMi1GIzYjLUZZNiRRIjJGJ0ZBLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GPjYtUSgmbWludXM7RidGQUZDRmluRkhGSkZMRk5GUC9GU1EsMC4yMjIyMjIyZW1GJy9GVkZdcC1GWTYkUSI1RidGQUZmbkZeb0Zmbi1GLDYlUSJ5RidGL0YyLUY+Ni1RIitGJ0ZBRkNGaW5GSEZKRkxGTkZQRlxwRl5wLUZZNiRRIjdGJ0ZBRmZuLUZcbzYlRmJwRmFvRmZvRmlvLUZZNiRRIzUyRidGQUZmbkZeb0ZlcC1GWTYkUSMyM0YnRkFGZm5GYnBGZXAtRlk2JFEjMTBGJ0ZBLUY+Ni1RIj1GJ0ZBRkNGaW5GSEZKRkxGTkZQL0ZTUSwwLjI3Nzc3NzhlbUYnL0ZWRmpxLUZZNiRGaG9GQUY9LUY2NiYtRiM2JUZeb0Y9RmJwRkEvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGQS1GPjYtUSI6RidGQUZDRmluRkhGSkZMRk5GUEZpcUZbcg==JSFH LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Abaixo, o comando detail fornece os resultados (em aritm\303\251tica exata) de an\303\241lises da elipse do Maple. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEpc2ltcGxpZnlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSdkZXRhaWxGJ0YvRjItRjY2JC1GIzYjLUYsNiVRIkVGJ0YvRjIvRjNRJ25vcm1hbEYnRkQ= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder 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 O \303\242ngulo de rota\303\247\303\243o entre os conjuntos de eixos n\303\243o \303\251 dado, e todos os dados s\303\243o dados apenas para o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjeHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-plano. Isso \303\251 assim, pode ser verificado atrav\303\251s da extra\303\247\303\243o das coordenadas dos focos, escrevendo elas em forma de ponto flutuante, e comparando os resultados com aqueles listados na Figura 2. Veja o c\303\241lculo abaixo. 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder NyQ3JCQiKy8uPWc3ISIqJCErRCw5P0JGJjckJCIrciFbPiY+ISIpJCIrW0x0YmtGJg== Tabela 2 An\303\241lise de uma quadr\303\241tica atrav\303\251s do comando ellipse no pacote geometry
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Student:-Precalculus:-ConicsTutor( ); Student:-Precalculus:-ConicsTutor( );
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Uma Receita para a Parametriza\303\247\303\243o Trigonom\303\251trica de uma Elipse</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= A equa\303\247\303\243o quadr\303\241tica geral em duas vari\303\241veis (digamos, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=) pode ser escrita na forma 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Calcule LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NDg7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEnJiM5NjM7RidGL0YyRjI=, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy, onde JSFH 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atrav\303\251s de um \303\242ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy, onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy \303\251 definido por 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjdXZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-termo. (Se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJjRidGL0YyRjk=, ent\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUScmIzk1MjtGJy8lJ2l0YWxpY0dGOEYvLUYzNi1RIj1GJ0YvRjZGOUY7Rj1GP0ZBRkMvRkZRLDAuMjc3Nzc3OGVtRicvRklGVC1JJm1mcmFjR0YkNigtRks2JVEnJiM5NjA7RidGTkYvLUYjNiVGKy9GT1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYW8vJSliZXZlbGxlZEdGOEYv ent\303\243o 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.) Deixamos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy ser dado pelo 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 onde a fun\303\247\303\243o arco-tangente de dois argumentos \303\251 usada para colocar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy no quadrante apropriado. Ent\303\243o, n\303\263s definimos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTUyO0YnRi9GMkYyRjItRiw2I1EhRidGPS1JI21vR0YkNi1RKCZlcXVpdjtGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVC1GLDYlUSJTRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRidGMg== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEkY29zRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTUyO0YnRi9GMkYyRjItRiw2I1EhRidGPS1JI21vR0YkNi1RKCZlcXVpdjtGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVC1GLDYlUSJDRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRidGMg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Os eixos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjdXZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-coordenadas s\303\243o rotacionados para os LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjWFlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-eixos, paralelos aos eixos de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjeHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-coordenadas, a partir da transforma\303\247\303\243o 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= O resultado \303\251 a equa\303\247\303\243o 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, onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYyLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJhRidGL0YyLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GVi1JJW1zdXBHRiQ2JS1GLDYlUSJDRidGL0YyLUYjNiUtSSNtbkdGJDYkUSIyRidGOUYvRjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GZW8tRiw2JVEiY0YnRi9GMkZSLUZZNiUtRiw2JVEiU0YnRi9GMkZobkZeb0Zhby1GLDYlUSJiRidGL0YyRlJGZW5GUkZccEY5 e 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 A forma padr\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkmbWZyYWNHRiQ2KC1GIzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y7USdub3JtYWxGJ0Y3RjovJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjdGOi1GIzYlLUYxNiUtRjQ2JVEnJiM5NDU7RicvRjhRJmZhbHNlRidGQ0Y9RkVGN0Y6LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZWLyUpYmV2ZWxsZWRHRlAtSSNtb0dGJDYtUSIrRidGQy8lJmZlbmNlR0ZQLyUqc2VwYXJhdG9yR0ZQLyUpc3RyZXRjaHlHRlAvJSpzeW1tZXRyaWNHRlAvJShsYXJnZW9wR0ZQLyUubW92YWJsZWxpbWl0c0dGUC8lJ2FjY2VudEdGUC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmlvLUYsNigtRjE2JS1GNDYlUSJZRidGN0Y6Rj1GRS1GIzYlLUYxNiUtRjQ2JVEnJiM5NDY7RidGT0ZDRj1GRUY3RjpGUUZURldGWS1GZm42LVEiPUYnRkNGaW5GW29GXW9GX29GYW9GY29GZW8vRmhvUSwwLjI3Nzc3NzhlbUYnL0ZbcEZecS1GQDYkRlNGQ0ZD \303\251 obtida atrav\303\251s da defini\303\247\303\243o 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 e 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 Consequentemente, a elipse dada \303\251 parametrizada pelas equa\303\247\303\265es JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tRiw2I1EhRidGPQ== 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 JSFH 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 JSFH 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 JSFH 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 JSFH 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHRjRGLy1GLDYtUSJ+RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSYwLjBlbUYnL0ZFRlAtRkc2JVEiU0YnL0ZLUSV0cnVlRicvRjBRJ2l0YWxpY0YnRkwtRkc2JVEkY29zRidGSkYvLUkobWZlbmNlZEdGJDYkLUYjNiQtRkc2JVEidEYnRlVGV0YvRi8tRiw2LVEiK0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yMjIyMjIyZW1GJy9GRUZiby1GRzYlUScmIzk0NjtGJ0ZKRi9GTC1GRzYlUSJDRidGVUZXRkwtRkc2JVEkc2luRidGSkYvRmZuRl5vLUZHNiVRImtGJ0ZVRldGLw==
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C\303\241lculos levando a uma parametriza\303\247\303\243o trigonom\303\251tricas de uma elipse
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Exemplo</Text-field> JSFH Vamos aplicar os c\303\241lculos da Tabela 3 para a quadr\303\241tica seguinte. Conforme a Tabela 3, bloqueamos os c\303\241lculos na Tabela 4. Entre com a quadr\303\241tica. 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O comando utilizado fornece o coeficiente de Taylor da pot\303\252ncia necess\303\241ria das vari\303\241veis. Desde que o comando \303\251 aplicado a uma quadr\303\241tica, o polin\303\264mio de Taylor de segundo grau \303\251 a quadr\303\241tica, ent\303\243o os coeficientes da quadr\303\241tica s\303\243o precisamente os coeficientes dos polin\303\264mios de Taylor dos graus adequados. 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JSFH Para verificar que a parametriza\303\247\303\243o \303\251 obtida na Tabela 4, realmente representa a elipse original, n\303\263s fornecemos a Figura 3 em que um gr\303\241fico impl\303\255cito da elipse est\303\241 sobreposto no gr\303\241fico param\303\251trico determinado pela parametriza\303\247\303\243o na Tabela 4. 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JSFH Figura 3 Gr\303\241fico impl\303\255cito da elipse determinada pela quadr\303\241tica sobreposta dada no gr\303\241fico de sua parametriza\303\247\303\243o. O gr\303\241fico impl\303\255cito est\303\241 em vermelho, a curva param\303\251trica, em preto.
JSFH
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Um Esbo\303\247o da Deriva\303\247\303\243o</Font></Text-field> JSFH Embora a Figura 3 sugere que a receita na Tabela 3 est\303\241 correta, \303\251 \303\272til derivar esses resultados. Para este fim, come\303\247amos de novo, com JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGTC8lJmRlcHRoR0ZVLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZRNiZGU0ZWRlgvRmVuUSVhdXRvRictRiw2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY8LUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZYLUYvNiVRImFGJ0YyRjUtRkQ2LVEifkYnRj5GR0ZKRkxGTkZQRlJGVC9GV1EmMC4wZW1GJy9GWkZcby1JJW1zdXBHRiQ2JS1GLzYlUSJ4RidGMkY1LUYjNiMtRjs2JFEiMkYnRj4vJTFzdXBlcnNjcmlwdHNoaWZ0R0ZCLUZENi1RIitGJ0Y+RkdGSkZMRk5GUEZSRlQvRldRLDAuMjIyMjIyMmVtRicvRlpGX3AtRi82JVEiYkYnRjJGNUZobkZhb0Zobi1GLzYlUSJ5RidGMkY1RltwLUYvNiVRImNGJ0YyRjVGaG4tRl9vNiVGZHBGZG9GaW9GW3AtRi82JVEiZEYnRjJGNUZobkZhb0ZbcC1GLzYlUSJlRidGMkY1RmhuRmRwRmhuRltwLUYvNiVRImZGJ0YyRjU= LC4qJkkiYUc2IiIiIkkieEdGJSIiI0YmKihJImJHRiVGJkYnRiZJInlHRiVGJkYmKiZJImNHRiVGJkYrRihGJiomSSJkR0YlRiZGJ0YmRiYqJkkiZUdGJUYmRitGJkYmSSJmR0YlRiY= O primeiro passo \303\251 a transla\303\247\303\243o 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, implementada como PiZJInFHNiI2IyIiIy1JJWV2YWxHJSpwcm90ZWN0ZWRHNiQmRiQ2IyIiIjckL0kieEdGJSwmSSJ1R0YlRi5JImhHRiVGLi9JInlHRiUsJkkidkdGJUYuSSJrR0YlRi4= LC4qJkkiYUc2IiIiIiwmSSJ1R0YlRiZJImhHRiVGJiIiI0YmKihJImJHRiVGJkYnRiYsJkkidkdGJUYmSSJrR0YlRiZGJkYmKiZJImNHRiVGJkYtRipGJiomSSJkR0YlRiZGJ0YmRiYqJkkiZUdGJUYmRi1GJkYmSSJmR0YlRiY= JSFH seguido pelo rearranjo PiZJInFHNiI2IyIiJC1JKGNvbGxlY3RHRiU2JSZGJDYjIiIjNyRJInVHRiVJInZHRiVJLGRpc3RyaWJ1dGVkR0Yl LDgqJkkiYUc2IiIiIkkidUdGJSIiI0YmKihJImJHRiVGJkYnRiZJInZHRiVGJkYmKiYsKEkiZEdGJUYmKiZGKkYmSSJrR0YlRiZGJiomRiRGJkkiaEdGJUYmRihGJkYnRiZGJiomSSJjR0YlRiZGK0YoRiYqJiwoKiZGNEYmRjBGJkYoKiZGKkYmRjJGJkYmSSJlR0YlRiZGJkYrRiZGJiomRiRGJkYyRihGJiomRjRGJkYwRihGJiomRjlGJkYwRiZGJiomRi5GJkYyRiZGJiooRipGJkYyRiZGMEYmRiZJImZHRiVGJg== Extraia os coeficientes de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= com QyU+JkkiRUc2IjYjIiIiLUkpY29lZnRheWxHRiY2JSZJInFHRiY2IyIiJC83JEkidUdGJkkidkdGJjckIiIhRjU3JEYoRjVGKD4mRiU2IyIiIy1GKjYlRixGMDckRjVGKA== LChJImRHNiIiIiIqJkkiYkdGJEYlSSJrR0YkRiVGJSomSSJhR0YkRiVJImhHRiRGJSIiIw== LCgqJkkiY0c2IiIiIkkia0dGJUYmIiIjKiZJImJHRiVGJkkiaEdGJUYmRiZJImVHRiVGJg== ent\303\243o, determine os valores de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= para que esses coeficientes desapare\303\247am. Isto \303\251 feito com JSFH PiZJInFHNiI2IyIiJS1JJnNvbHZlR0YlNiQ8JC8mSSJFR0YlNiMiIiIiIiEvJkYuNiMiIiNGMTwkSSJoR0YlSSJrR0Yl PCQvSSJoRzYiKiYsJiomSSJiR0YlIiIiSSJlR0YlRipGKiomSSJjR0YlRipJImRHRiVGKiEiI0YqLCYqJEYpIiIjISIiKiZGLUYqSSJhR0YlRioiIiVGMy9JImtHRiUsJComLCYqJkYuRipGKUYqRjMqJkY1RipGK0YqRjJGKkYwRjNGMw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Aplicando essas defini\303\247\303\265es de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= coloque a quadr\303\241tica na forma QyU+JkkicUc2IjYjIiImLUkpc2ltcGxpZnlHRiY2Iy1JJWV2YWxHJSpwcm90ZWN0ZWRHNiQmRiU2IyIiJCZGJTYjIiIlISIiPiZGJTYjIiInLUkoY29sbGVjdEc2JEYuSShfc3lzbGliR0YmNiZGJDckSSJ1R0YmSSJ2R0YmSSxkaXN0cmlidXRlZEdGJkYq LCoqJkkiYUc2IiIiIkkidUdGJSIiI0YmKihJImJHRiVGJkYnRiZJInZHRiVGJkYmKiZJImNHRiVGJkYrRihGJiomLCwqKEYqRiZJImVHRiVGJkkiZEdGJUYmRiYqJkYkRiZGMUYoISIiKihGJEYmRi1GJkkiZkdGJUYmIiIlKiZGLUYmRjJGKEY0KiZGNkYmRipGKEY0RiYsJiokRipGKEY0KiZGLUYmRiRGJkY3RjRGJg== O termo constante, nomeadamente, PiZJInFHNiI2IyIiKC1JKWNvZWZ0YXlsRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiUmRiQ2IyIiJy83JEkidUdGJUkidkdGJTckIiIhRjZGNQ== KiYsLCooSSJiRzYiIiIiSSJlR0YmRidJImRHRiZGJ0YnKiZJImFHRiZGJ0YoIiIjISIiKihGK0YnSSJjR0YmRidJImZHRiZGJyIiJSomRi9GJ0YpRixGLSomRjBGJ0YlRixGLUYnLCYqJEYlRixGLSomRi9GJ0YrRidGMUYt sugere definindo PkkkcGhpRzYiLCYqJEkiYkdGJCIiIyIiIiomSSJjR0YkRilJImFHRiRGKSEiJQ== LCYqJEkiYkc2IiIiIyIiIiomSSJjR0YlRidJImFHRiVGJyEiJQ== e o determinante PkkmZGVsdGFHNiItSSxEZXRlcm1pbmFudEc2JC9JK21vZHVsZW5hbWVHRiRJLkxpbmVhckFsZ2VicmFHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiRGLDYjLUknTWF0cml4R0YkNiMvSSQlaWRHRiQiKiM+WnRe LCwqJkkiYUc2IiIiIkkiZUdGJSIiIyEiIyooRiRGJkkiY0dGJUYmSSJmR0YlRiYiIikqKEkiYkdGJUYmRidGJkkiZEdGJUYmRigqJkYsRiZGL0YoRikqJkYrRiZGMEYoRik= Se n\303\263s definirmos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy como 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 atrav\303\251s de PkkkcmhvRzYiLCQqJkkmZGVsdGFHRiQiIiJJJHBoaUdGJCEiIiNGKCIiIw== LCQqJiwsKiZJImFHNiIiIiJJImVHRiciIiMhIiMqKEYmRihJImNHRidGKEkiZkdGJ0YoIiIpKihJImJHRidGKEYpRihJImRHRidGKEYqKiZGLkYoRjFGKkYrKiZGLUYoRjJGKkYrRigsJiokRjFGKkYoKiZGLUYoRiZGKCEiJSEiIiNGKEYq ent\303\243o, o termo constante torna-se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtaUdGJDYlUScmIzk2MTtGJy8lJ2l0YWxpY0dGNEYvRi8=, como vemos em LUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmJkkicUdGJzYjIiIoIiIiSSRyaG9HRidGLg== IiIh Neste ponto, a quadr\303\241tica pode ser posta na forma PiZJInFHNiI2IyIiKSwmLUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywmJkYkNiMiIiciIiJJJHJob0dGJUYzRjNJIlJHRiUhIiI= LCoqJkkiYUc2IiIiIkkidUdGJSIiI0YmKihJImJHRiVGJkYnRiZJInZHRiVGJkYmKiZJImNHRiVGJkYrRihGJkkiUkdGJSEiIg== onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= tem que ser usado no lugar de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEmJnJobztGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn desde que uma express\303\243o j\303\241 foi atribu\303\255da a LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEmJnJobztGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn. Para usar LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEmJnJobztGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn nesta forma da quadr\303\241tica, a atribui\303\247\303\243o deve ser removida com LUkpdW5hc3NpZ25HNiI2Iy5JJHJob0dGJA== ent\303\243o podemos escrever PiZJInFHNiI2IyIiKi1JJWV2YWxHJSpwcm90ZWN0ZWRHNiQmRiQ2IyIiKS9JIlJHRiVJJHJob0dGJQ== LCoqJkkiYUc2IiIiIkkidUdGJSIiI0YmKihJImJHRiVGJkYnRiZJInZHRiVGJkYmKiZJImNHRiVGJkYrRihGJkkkcmhvR0YlISIi O LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjdXZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-termo \303\251 removido com uma rota\303\247\303\243o do LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjdXZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-sistema para um LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjWFlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-sstema atrav\303\251s de equa\303\247\303\265es 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Usando as abrevia\303\247\303\265es LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSRjb3NGJy9GMEY9RjktSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUScmIzk1MjtGJ0ZSRjlGOUY5Rjk= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSRzaW5GJy9GMEY9RjktSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUScmIzk1MjtGJ0ZSRjlGOUY5Rjk=, a quadr\303\241tica torna-se PiZJInFHNiI2IyIjNS1JJWV2YWxHJSpwcm90ZWN0ZWRHNiQmRiQ2IyIiKjckL0kidUdGJSwmKiZJIkNHRiUiIiJJIlhHRiVGNUY1KiZJIlNHRiVGNUkiWUdGJUY1ISIiL0kidkdGJSwmKiZGOEY1RjZGNUY1KiZGNEY1RjlGNUY1 LCoqJkkiYUc2IiIiIiwmKiZJIkNHRiVGJkkiWEdGJUYmRiYqJkkiU0dGJUYmSSJZR0YlRiYhIiIiIiNGJiooSSJiR0YlRiZGJ0YmLCYqJkYsRiZGKkYmRiYqJkYpRiZGLUYmRiZGJkYmKiZJImNHRiVGJkYyRi9GJkkkcmhvR0YlRi4= ou equivalentemente, PiZJInFHNiI2IyIjNi1JKGNvbGxlY3RHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JSZGJDYjIiM1NyRJIlhHRiVJIllHRiVJLGRpc3RyaWJ1dGVkR0Yl LCoqJiwoKiZJImFHNiIiIiJJIkNHRiciIiNGKComSSJjR0YnRihJIlNHRidGKkYoKihJImJHRidGKEYpRihGLUYoRihGKEkiWEdGJ0YqRigqKCwqKiZGL0YoRi1GKiEiIiomRi9GKEYpRipGKCooRiZGKEYtRihGKUYoISIjKihGLEYoRi1GKEYpRihGKkYoSSJZR0YnRihGMEYoRihJJHJob0dGJ0Y0KiYsKComRiZGKEYtRipGKComRixGKEYpRipGKEYuRjRGKEY5RipGKA== Os coeficientes de 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 s\303\243o respectivamente Qyc+JkkicUc2IjYjIiM3LUkpY29lZnRheWxHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2JSZGJTYjIiM2LzckSSJYR0YmSSJZR0YmNyQiIiFGNzckIiIjRjciIiI+JkYlNiMiIzgtRio2JUYvRjI3JEY6RjpGOj4mRiU2IyIjOS1GKjYlRi9GMjckRjdGOQ== LCgqJkkiYUc2IiIiIkkiQ0dGJSIiI0YmKiZJImNHRiVGJkkiU0dGJUYoRiYqKEkiYkdGJUYmRidGJkYrRiZGJg== LCoqJkkiYkc2IiIiIkkiU0dGJSIiIyEiIiomRiRGJkkiQ0dGJUYoRiYqKEkiYUdGJUYmRidGJkYrRiYhIiMqKEkiY0dGJUYmRidGJkYrRiZGKA== 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LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEoJnRoZXRhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= para que o coeficiente de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJZRidGL0YyRjVGOQ==desapare\303\247a, um processo auxiliado por colocar a equa\303\247\303\243o resultante para a forma 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 ou 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 a partir da qual segue-se que 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 e, portanto, que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUkjbW5HRiQ2JFEiMkYnRjItSSNtb0dGJDYtUSJ+RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlItRiw2JVEnJiM5NTI7RidGL0YyRjJGMi1GPzYtUSI9RidGMkZCRkRGRkZIRkpGTEZOL0ZRUSwwLjI3Nzc3NzhlbUYnL0ZURmZuLUkmbWZyYWNHRiQ2KC1GLDYlUSJiRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRiM2Jy1GLDYlUSJhRidGXm9GYG8tRj82LVEoJm1pbnVzO0YnRjJGQkZERkZGSEZKRkxGTi9GUVEsMC4yMjIyMjIyZW1GJy9GVEZbcC1GLDYlUSJjRidGXm9GYG9GXm9GYG8vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmVwLyUpYmV2ZWxsZWRHRjFGMg== Uma implementa\303\247\303\243o do Maple destas \303\272ltimas manipula\303\247\303\265es \303\251 entediante. Ela come\303\247a com a equa\303\247\303\243o PiZJInFHNiI2IyIjOi8mRiQ2IyIjOCIiIQ== LywqKiZJImJHNiIiIiJJIlNHRiYiIiMhIiIqJkYlRidJIkNHRiZGKUYnKihJImFHRiZGJ0YoRidGLEYnISIjKihJImNHRiZGJ0YoRidGLEYnRikiIiE= e exige que se deslocam os termos contendo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= para a direita com PiZJInFHNiI2IyIjOy1JIitHJSpwcm90ZWN0ZWRHNiQmRiQ2IyIjOiwmKiZJImJHRiUiIiJJIlNHRiUiIiNGMiomRjFGMkkiQ0dGJUY0ISIi LywmKihJImFHNiIiIiJJIlNHRiZGJ0kiQ0dGJkYnISIjKihJImNHRiZGJ0YoRidGKUYnIiIjLCYqJkkiYkdGJkYnRihGLUYnKiZGMEYnRilGLSEiIg== Esta equa\303\247\303\243o \303\251 ent\303\243o multiplicada por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGL0Yv, Obtendo-se PiZJInFHNiI2IyIjPCwkJkYkNiMiIzshIiI= LywmKihJImFHNiIiIiJJIlNHRiZGJ0kiQ0dGJkYnIiIjKihJImNHRiZGJ0YoRidGKUYnISIjLCYqJkkiYkdGJkYnRihGKiEiIiomRjBGJ0YpRipGJw== que fatora para PiZJInFHNiI2IyIjPS8tSSdmYWN0b3JHRiU2Iy1JJGxoc0clKnByb3RlY3RlZEc2IyZGJDYjIiM8LUkoY29sbGVjdEc2JEYuSShfc3lzbGliR0YlNiQtSSRyaHNHRi5GL0kiYkdGJQ== LywkKihJIkNHNiIiIiJJIlNHRiZGJywmSSJhR0YmRidJImNHRiYhIiJGJyIiIyomLCYqJEYoRi1GLCokRiVGLUYnRidJImJHRiZGJw== Removendo as abrevia\303\247\303\265es LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= leva a PiZJInFHNiI2IyIjPi1JJWV2YWxHJSpwcm90ZWN0ZWRHNiQmRiQ2IyIjPTckL0kiQ0dGJS1JJGNvc0dGJTYjSSZ0aGV0YUdGJS9JIlNHRiUtSSRzaW5HRiVGNA== LywkKigtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kmdGhldGFHRioiIiItSSRzaW5HRidGK0YtLCZJImFHRipGLUkiY0dGKiEiIkYtIiIjKiYsJiokRi5GNEYzKiRGJUY0Ri1GLUkiYkdGKkYt que pode ser escrita como PiZJInFHNiI2IyIjPy1JJ2ZhY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLUkoY29tYmluZUdGJTYjJkYkNiMiIz4= LyomLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJEkmdGhldGFHRikiIiMiIiIsJkkiYUdGKUYuSSJjR0YpISIiRi4qJi1JJGNvc0dGJkYqRi5JImJHRilGLg== A express\303\243o para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUkjbW5HRiQ2JFEiMkYnRjItSSNtb0dGJDYtUSJ+RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlItRiw2JVEoJnRoZXRhO0YnRi9GMkYyRjJGMg==aparece depois de um rearranjo e convers\303\243o final atrav\303\251s de LUkoY29udmVydEclKnByb3RlY3RlZEc2JCooJkkicUc2IjYjIiM/IiIiLCZJImFHRilGLEkiY0dGKSEiIkYwLUkkY29zRzYkRiRJKF9zeXNsaWJHRik2IywkSSZ0aGV0YUdGKSIiI0YwSSR0YW5HRjM= Ly1JJHRhbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCRJJnRoZXRhR0YoIiIjKiYsJkkiYUdGKCIiIkkiY0dGKCEiIkYySSJiR0YoRjA= O \303\242ngulo LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEoJnRoZXRhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= determinado por esta equa\303\247\303\243o pode ser no primeiro ou segundo quadrante. Quando ele est\303\241 no primeiro quadrante, tanto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTUyO0YnRi9GMkYyRjJGMg== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkY29zRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTUyO0YnRi9GMkYyRjJGMg== s\303\243o positivos, quando \303\251 no segunda, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkY29zRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRKCZ0aGV0YTtGJ0YvRjJGMkYyRjI= ser\303\241 negativo. Assim, o cuidado deve ser tomado quando determinar LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEoJnRoZXRhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=. Com o coeficiente do LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjWFlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn-termo definido para zero, a quadr\303\241tica, o lado esquerdo de uma equa\303\247\303\243o cujo lado direito \303\251 zero, torna-se 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 e, portanto, 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 As defini\303\247\303\265es 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 e 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 completa a deriva\303\247\303\243o das f\303\263rmulas. 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