Question

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

Foci (±3, 0), a = 4

Answer 1

Foci (±3, 0), a = 4

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, c = 3 and a = 4

It is known that a² = b² + c²

∴ 4² = b² + 3²

= 16 = b² + 9

= b² = 16 - 9 = 7

Thus, the equation of the ellipse is `x^2/16 + y^2/7 = 1`.