onsidere a equação da elipse 16 x + 4 y -256=0 obtenha os vertices do eixo maior e sua excentricidade, essa aqui cheguei a1 = 0,-8 e a2 = 0,8 e excentricidade ta me matando nao consigo chegar no resultado pode me ajudar ??
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Boa tarde!
Solução!
Equação da elipse!
![\dfrac{ x^{2} }{a^{2} }+ \dfrac{y^{2} }{b^{2} }=1\\\\\\\\
a\ \textgreater \ b~~O~~eixo~~maior~~esta~~contido~~em~~x\\\\\\\
b\ \textgreater \ a~~O~~eixo~~maior~~esta~~contido~~em~~y](https://tex.z-dn.net/?f=+%5Cdfrac%7B+x%5E%7B2%7D+%7D%7Ba%5E%7B2%7D+%7D%2B+%5Cdfrac%7By%5E%7B2%7D+%7D%7Bb%5E%7B2%7D+%7D%3D1%5C%5C%5C%5C%5C%5C%5C%5C%0Aa%5C+%5Ctextgreater+%5C+b%7E%7EO%7E%7Eeixo%7E%7Emaior%7E%7Eesta%7E%7Econtido%7E%7Eem%7E%7Ex%5C%5C%5C%5C%5C%5C%5C%0Ab%5C+%5Ctextgreater+%5C+a%7E%7EO%7E%7Eeixo%7E%7Emaior%7E%7Eesta%7E%7Econtido%7E%7Eem%7E%7Ey+ "\dfrac{ x^{2} }{a^{2} }+ \dfrac{y^{2} }{b^{2} }=1\\\\\\\\
a\ \textgreater \ b~~O~~eixo~~maior~~esta~~contido~~em~~x\\\\\\\
b\ \textgreater \ a~~O~~eixo~~maior~~esta~~contido~~em~~y")
![16 x^{2} +4y^{2}-256=0\\\\\\\
16 x^{2} +4y^{2}=256\\\\\\\
\dfrac{16 x^{2} }{256}+ \dfrac{4y^{2} }{256}= \dfrac{256}{256}\\\\\\\\
\dfrac{ x^{2} }{16}+ \dfrac{y^{2} }{64}=1\\\\\\\\
Veja!\\\\\
b\ \textgreater \ a\\\\\\\
Vertice= \sqrt{64}\\\\
Vertice=\pm8\\\\\\
V1(0,8)\\\\\\\
V2(0,-8)](https://tex.z-dn.net/?f=16+x%5E%7B2%7D+%2B4y%5E%7B2%7D-256%3D0%5C%5C%5C%5C%5C%5C%5C%0A16+x%5E%7B2%7D+%2B4y%5E%7B2%7D%3D256%5C%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B16+x%5E%7B2%7D+%7D%7B256%7D%2B+%5Cdfrac%7B4y%5E%7B2%7D+%7D%7B256%7D%3D+%5Cdfrac%7B256%7D%7B256%7D%5C%5C%5C%5C%5C%5C%5C%5C%0A+++%5Cdfrac%7B+x%5E%7B2%7D+%7D%7B16%7D%2B+%5Cdfrac%7By%5E%7B2%7D+%7D%7B64%7D%3D1%5C%5C%5C%5C%5C%5C%5C%5C%0AVeja%21%5C%5C%5C%5C%5C%0Ab%5C+%5Ctextgreater+%5C+a%5C%5C%5C%5C%5C%5C%5C%0AVertice%3D++%5Csqrt%7B64%7D%5C%5C%5C%5C%0AVertice%3D%5Cpm8%5C%5C%5C%5C%5C%5C%0A%0AV1%280%2C8%29%5C%5C%5C%5C%5C%5C%5C%0AV2%280%2C-8%29+%0A++ "16 x^{2} +4y^{2}-256=0\\\\\\\
16 x^{2} +4y^{2}=256\\\\\\\
\dfrac{16 x^{2} }{256}+ \dfrac{4y^{2} }{256}= \dfrac{256}{256}\\\\\\\\
\dfrac{ x^{2} }{16}+ \dfrac{y^{2} }{64}=1\\\\\\\\
Veja!\\\\\
b\ \textgreater \ a\\\\\\\
Vertice= \sqrt{64}\\\\
Vertice=\pm8\\\\\\
V1(0,8)\\\\\\\
V2(0,-8)")
![b^{2}=a^{2}+c^{2}\\\\\\
8^{2}=4^{2}+ c^{2}\\\\\\
64=16+ c^{2}\\\\\\
48=c^{2}\\\\\\
c= \sqrt{48} \\\\\\
c=4 \sqrt{3}\\\\\\\\\
e= \frac{4 \sqrt{3} }{4} \\\\\\\
\boxed{e= \sqrt{3} }](https://tex.z-dn.net/?f=b%5E%7B2%7D%3Da%5E%7B2%7D%2Bc%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0A8%5E%7B2%7D%3D4%5E%7B2%7D%2B+c%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0A64%3D16%2B+c%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0A48%3Dc%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0Ac%3D+%5Csqrt%7B48%7D+%5C%5C%5C%5C%5C%5C%0Ac%3D4+%5Csqrt%7B3%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0Ae%3D+%5Cfrac%7B4+%5Csqrt%7B3%7D+%7D%7B4%7D+%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Be%3D+%5Csqrt%7B3%7D+%7D+%0A++++ "b^{2}=a^{2}+c^{2}\\\\\\
8^{2}=4^{2}+ c^{2}\\\\\\
64=16+ c^{2}\\\\\\
48=c^{2}\\\\\\
c= \sqrt{48} \\\\\\
c=4 \sqrt{3}\\\\\\\\\
e= \frac{4 \sqrt{3} }{4} \\\\\\\
\boxed{e= \sqrt{3} }")
Boa noite!
Bons estudos!
Solução!
Equação da elipse!
Boa noite!
Bons estudos!
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