Question

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

Length of major axis 26, foci (±5, 0)

Answer 1

Length of major axis = 26; foci = (±5, 0).

Since the foci are on the x-axis, the major axis is along 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, 2a = 26 = 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^2/13^2 + y^2/12^2 = 1` or  `x^2/169 + y^2/144 = 1`.