anonymous
  • anonymous
Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
since the foci are at \((0,-2)\) and \((0,2)\) the center is at the origin, so at least we know it looks like \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]
anonymous
  • anonymous
since the vertices are at \((0,-5)\) and \((0,5)\) we know \(b=5\) and so \(b^2=25\)
anonymous
  • anonymous
Thank you

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anonymous
  • anonymous
we still need \(a^2\) but since \(2^2=b^2-a^2\) we can solve for it
anonymous
  • anonymous
\(a^2=25-4=21\)
anonymous
  • anonymous
let me make sure this is right before i tell you something silly
anonymous
  • anonymous
yes, i think this works, i.e. the answer would be \[\frac{x^2}{21}+\frac{y^2}{25}=1\]
anonymous
  • anonymous
lets check it http://www.wolframalpha.com/input/?i=ellipse+x^2%2F21%2By^2%2F25%3D1
anonymous
  • anonymous
i had a multiple choice answer, and when you told me 25 was b^2, it was the only option. you are right, it is x^2/21 + y^2/25 = 1
anonymous
  • anonymous
oh, hiding that information... well it works in any case

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