Determine the Appropriate Rotation Formulas to Use So That the New

Multiple Choice

Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.
- $$4 x ^ { 2 } + 6 x y + 4 y ^ { 2 } - 8 x + 8 y = 0$$

A) $x = \frac { u } { \sqrt { 2 } } - \frac { v } { \sqrt { 2 } }$ and $y = \frac { u } { \sqrt { 2 } } + \frac { v } { \sqrt { 2 } }$
B) $x = \frac { 1 } { 2 } u - \frac { \sqrt { 3 } } { 2 } v$ and $y = \frac { \sqrt { 3 } } { 2 } u + \frac { 1 } { 2 } v$
C) $x = - v$ and $y = u$
D) $x = \frac { u } { \sqrt { 2 } } + \frac { v } { \sqrt { 2 } }$ and $y = \frac { u } { \sqrt { 2 } } - \frac { v } { \sqrt { 2 } }$