Rotate the Axes to Eliminate the Xy-Term in the Following $$3 x ^ { 2 } - 12 x y + 12 y ^ { 2 } + 15 \sqrt { 5 } y + 3 = 0$$

Multiple Choice

Rotate the axes to eliminate the xy-term in the following equation and then write the equation in standard form. $$3 x ^ { 2 } - 12 x y + 12 y ^ { 2 } + 15 \sqrt { 5 } y + 3 = 0$$

A) $\left( x ^ { \prime } - 1 \right) ^ { 2 } = 3 \left( y ^ { \prime } - \frac { 4 } { 5 } \right)$
B) $\left( x ^ { \prime } + 3 \right) ^ { 2 } = - 5 \left( y ^ { \prime } + \frac { 1 } { 3 } \right)$
C) $\left( y ^ { \prime } + 1 \right) ^ { 2 } = - \left( x ^ { \prime } - \frac { 4 } { 5 } \right)$
D) $\left( y ^ { \prime } - \frac { 4 } { 5 } \right) ^ { 2 } = 3 \left( x ^ { \prime } - 1 \right)$
E) $\left( y ^ { \prime } + \frac { 4 } { 5 } \right) ^ { 2 } = x ^ { \prime } + \frac { 1 } { 3 }$