Question

Find the equation of ellipse whose vertices are at (±6, 0) and foci at (±4, 0).

Answer 1

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

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

Given: vertices of ellipse (±6, 0)

Here a = 6

Again,

Foci is of the form (±c, 0)

Given: foci of ellipse at (±4, 0)

⇒ c = 4

Find b:

We know, c² = a² – b²

16 = 36 – b²

or b² = 20

Equation (1)⇒

x²/36 + y²/20 = 1

Which is required equation.