Because of the Forces Caused by Its Rotation, a Planet $( z = 0 )$

Multiple Choice

Because of the forces caused by its rotation, a planet is actually an oblate ellipsoid rather than a sphere. The equatorial radius is 3961 miles and the polar radius is 3957 miles. Find an equation of the ellipsoid. Assume that the center of a planet is at the origin and the xy- trace $( z = 0 )$ corresponds to the equator.

A) $\frac { x ^ { 2 } } { 3961 ^ { 2 } } + \frac { y ^ { 2 } } { 3961 ^ { 2 } } - \frac { z ^ { 2 } } { 3957 ^ { 2 } } = 1$
B) $\frac { x ^ { 2 } } { 3961 ^ { 2 } } + \frac { y ^ { 2 } } { 3957 ^ { 2 } } + \frac { z ^ { 2 } } { 3961 ^ { 2 } } = 1$
C) $\frac { x ^ { 2 } } { 3961 ^ { 2 } } + \frac { y ^ { 2 } } { 3961 ^ { 2 } } + \frac { z ^ { 2 } } { 3957 ^ { 2 } } = 1$
D) $\frac { x ^ { 2 } } { 3961 ^ { 2 } } - \frac { y ^ { 2 } } { 3961 ^ { 2 } } - \frac { z ^ { 2 } } { 3957 ^ { 2 } } = 1$
E) $\frac { x ^ { 2 } } { 3961 ^ { 2 } } + \frac { y ^ { 2 } } { 3957 ^ { 2 } } + \frac { z ^ { 2 } } { 3957 ^ { 2 } } = 1$