Question

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

Vertices (±6, 0), foci (±4, 0)

Answer 1

Vertices (±6, 0), foci (±4, 0)

Here, the vertices are on the x-axis.

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

Accordingly, a = 6 and c = 4

It is known that a² = b² + c²

∴ 6² = b² + 4²

= 36 = b² + 16

= b² = 36 - 16

= b = `sqrt20`

Thus, the equation of the ellipse is `x^2/6^2 + y^2/(sqrt(20))^2 = 1` or `x^2/36 + y^2/20 = 1`.