Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5

Question

anonymous · Answer

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 · Answer

since the vertices are at $(0,-5)$ and $(0,5)$ we know $b=5$ and so $b^2=25$

anonymous · Answer

Thank you

anonymous · Answer

we still need $a^2$ but since $2^2=b^2-a^2$ we can solve for it

anonymous · Answer

$a^2=25-4=21$

anonymous · Answer

let me make sure this is right before i tell you something silly

anonymous · Answer

yes, i think this works, i.e. the answer would be 
$$\frac{x^2}{21}+\frac{y^2}{25}=1$$

anonymous · Answer

anonymous · Answer

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 · Answer

oh, hiding that information... well it works in any case