## alyssababy7 2 years ago Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5

1. satellite73

since the foci are at $$(0,-2)$$ and $$(0,2)$$ the center is at the origin, so at least we know it looks like $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

2. satellite73

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

3. alyssababy7

Thank you

4. satellite73

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

5. satellite73

$$a^2=25-4=21$$

6. satellite73

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

7. satellite73

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

8. satellite73
9. alyssababy7

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

10. satellite73

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