Classify the Surface $$25 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 y + 2 z = 0$$

Multiple Choice

Classify the surface.
$$25 x ^ { 2 } + y ^ { 2 } - z ^ { 2 } - 2 y + 2 z = 0$$
Select the correct answer.

A) A hyperboloid of one sheet with center $( - 3,0,1 )$ and axis parallel to the $z$ -axis.
B) A circular paraboloid with vertex $( 0,3,1 )$ and axis the $z$ -axis.
C) A cone with axis parallel to the $z$ -axis and vertex $( 0,1,1 )$ .