Question

Find the equation for the ellipse that satisfies the given conditions:

Vertices (0, ±13), foci (0, ±5)

Answer 1

Vertices (0, ±13), foci (0, ±5)

Here, the vertices are on the y-axis.

Therefore, the equation of the ellipse will be of the form `x^2/b^2 + y^2/a^2` = 1, where a is the semi-major axis.

Accordingly, a = 13 and c = 5

It is known that a² = b² + c²

∴ 13² = b² + 5²

= 169 = b² + 25

= b² = 169 - 25

= b = `sqrt144` = 12

Thus, the equation of the ellipse is `x^2/12^2 + y^2/13^2 = 1` or `x^2/144 + y^2/169 = 1`.