Question

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

b = 3, c = 4, centre at the origin; foci on the x axis.

Answer 1

It is given that b = 3, c = 4, centre at the origin; foci on the x axis.

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, b = 3, c = 4.

It is known that a² = b² + c²

∴ a² = 3² + 4² = 9 + 16 = 25

= a = 5

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