Find an Equation for the Surface Obtained by Rotating the Parabola

Multiple Choice

Find an equation for the surface obtained by rotating the parabola $y = 2 x ^ { 2 }$ about the $y$ -axis.
Select the correct answer.

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