An Ellipsoid Is Created by Rotating the Ellipse $4 x ^ { 2 } + y ^ { 2 } = 16$

Multiple Choice

An ellipsoid is created by rotating the ellipse $4 x ^ { 2 } + y ^ { 2 } = 16$ about the x-axis. Find the equation of the ellipsoid.

A) $16 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1$
B) $4 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 16$
C) $4 x ^ { 2 } - y ^ { 2 } + z ^ { 2 } = 16$
D) $4 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 1$
E) $$4 x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$$