Question

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

Vertices (±5, 0), foci (±4, 0)

Answer 1

Vertices (±5, 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 = 5 and c = 4

It is known that a² = b² + c²

∴ 5² = b² + 4²

= 25 = b² + 16

= b² = 25 - 16

= b = `sqrt9` = 3

Thus, the equation of the ellipse is `x^2/5^2 + y^2/3^2 = 1` or `x^2/25 + y^2/9 = 1`.