Use Axis of Rotation Formulas for X and Y to Transform

Multiple Choice

Use axis of rotation formulas for x and y to transform the quadratic equation to an equation in (u, v) coordinates with no
cross-product term.
- $$2 x ^ { 2 } + 2 \sqrt { 3 } x y + 4 y ^ { 2 } - 8 = 0$$

A) $\frac { \mathrm { u } ^ { 2 } } { 8 } + \frac { 5 \mathrm { v } ^ { 2 } } { 8 } = 1$
B) $\frac { 5 \mathrm { u } ^ { 2 } } { 8 } + \frac { \mathrm { v } ^ { 2 } } { 8 } = 1$
C) $\frac { 2 u ^ { 2 } } { 8 } + \frac { v ^ { 2 } } { 8 } = 1$
D) $\frac { 3 \mathrm { u } ^ { 2 } } { 16 } + \frac { \mathrm { v } ^ { 2 } } { 16 } = 1$