Rotate the Axes to Eliminate The $x y$ -Term in the Following Equation

Multiple Choice

Rotate the axes to eliminate the $x y$ -term in the following equation.
$$18 x ^ { 2 } - 12 \sqrt { 3 } x y + 6 y ^ { 2 } + 12 x + 12 \sqrt { 3 } y = 0$$

A) $\left( y ^ { \prime } \right) ^ { 2 } + x ^ { \prime } = 0$
B) $6 \sqrt { 3 } \left( y ^ { \prime } \right) ^ { 2 } + 6 \sqrt { 3 } x ^ { \prime } = 0$
C) $6 \left( x ^ { \prime } \right) ^ { 2 } - 6 y ^ { \prime } = 0$
D) $\frac { \left( y ^ { \prime } \right) ^ { 2 } } { 6 } + \frac { x ^ { \prime } } { 6 } = 0$
E) $\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 12 } + \frac { y ^ { \prime } } { 12 } = 0$