Find an equation for the ellipse that satisfies the given conditions.?

Question

Find an equation for the ellipse that satisfies the given conditions.

Foci: F(0, ±4), vertices: (0, ±5)

Answer 1

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So it's centered at (0 , 0), obviously

(x - 0)^2 / a^2 + (y - 0)^2 / b^2 = 1

x^2 / a^2 + y^2 / b^2 = 1

We know that it passes through (0 , -5) and (0 , 5)

0^2 / a^2 + (+/- 5)^2 / b^2 = 1

25/b^2 = 1

25 = b^2

5 = b

x^2 / a^2 + y^2 / 25 = 1

F = sqrt(25 - a^2)

F = 4

4 = sqrt(25 - a^2)

16 = 25 - a^2

a^2 = 9

a = 3

x^2 / 9 + y^2 / 25 = 1

25x^2 + 9x^2 = 225