Question

Find the equation of ellipse whose vertices are at (0, ±4) and foci at (0, ±√7).

Answer 1

Vertices are of the form (0, ±a), hence major axis is along x-axis.

So, the equation is of the form: x²/b² + y²/a² = 1 …..(1)

Given: vertices of ellipse (0, ±4)

Here a = 4

Again,

Foci is of the form (0, ±c)

Given: foci of ellipse at (0, ±√7)

⇒ c = √7

Find b:

We know, c² = a² – b²

7 = 16 – b²

or b² = 9

Equation (1)⇒

x²/9 + y²/16 = 1

Which is required equation.