Question

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

Length of minor axis 16, foci (0, ±6)

Answer 1

Length of minor axis = 16; foci = (0, ±6).

Since the foci are on the y-axis, the major axis is along the y-axis.

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

Accordingly, 2b = 16 = b = 8 and c = 6

It is known that a² = b² + c²

∴ a2 = 8² + 6² = 64 + 36 = 100

= a = `sqrt100` = 10

Thus, the equation of the ellipse is `x^2/8^2 + y^2/10^2 = 1` or  `x^2/64 + y^2/100 = 1`.