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) $z ^ { 2 } + 3 x ^ { 2 } + y ^ { 2 } = 1$

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The Answer of 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) $z ^ { 2 } + 3 x ^ { 2 } + y ^ { 2 } = 1$

Find an Equation for the Surface Obtained by Rotating the Parabola