Find an Equation for the Surface Obtained by Rotating the Parabola

Multiple Choice

Find an equation for the surface obtained by rotating the parabola $y = 3 x ^ { 2 }$ about the $y$ -axis.

A) $z ^ { 2 } - 3 x ^ { 2 } - y ^ { 2 } = 1$
B) $y ^ { 2 } + 3 x ^ { 2 } = z$
C) $z ^ { 2 } - 3 x ^ { 2 } = y$
D) $3 z ^ { 2 } + 3 x ^ { 2 } = y$
E) $z ^ { 2 } + 3 x ^ { 2 } + y ^ { 2 } = 1$