Complete the Square to Determine the Type of Curve Represented $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

Multiple Choice

Complete the square to determine the type of curve represented by the equation. $x ^ { 2 } + 6 x - 3 y ^ { 2 } + 12 y = 12$

A) $( x + 2 ) ^ { 2 } = 9 ( y - 3 )$
, parabola
B) $\frac { ( x + 2 ) ^ { 2 } } { 81 } + \frac { ( y - 3 ) ^ { 2 } } { 16 } = 1$
, ellipse
C) $\frac { ( x + 2 ) ^ { 2 } } { 8 } - \frac { ( y - 3 ) ^ { 2 } } { 4 } = 1$
, hyperbola
D) $\frac { ( x + 3 ) ^ { 2 } } { 9 } - \frac { ( y - 2 ) ^ { 2 } } { 3 } = 1$
, hyperbola
E) none of these