Classify the Surface $23 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 12 y + 12 z = 0$

Multiple Choice

Classify the surface. $23 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 12 y + 12 z = 0$

A) A hyperboloid of one sheet with center $( - 8,0,6 )$ and axis parallel to the z-axis.
B) A cone with axis parallel to the z-axis and vertex $( 0,6,6 )$ .
C) A circular paraboloid with vertex $( 0,8,6 )$ and axis the z-axis.