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.
- $$x ^ { 2 } + 2 x y + y ^ { 2 } + 4 \sqrt { 2 } x - 4 \sqrt { 2 } y = 0$$

A) $\frac { 3 u ^ { 2 } } { 8 } + \frac { v ^ { 2 } } { 8 } = 1$
B) $\mathrm { v } = \frac { \mathrm { u } 2 } { 4 }$
C) $\frac { \mathrm { u } ^ { 2 } } { 4 } + \frac { 3 \mathrm { v } ^ { 2 } } { 4 } = 1$
D) $4 u = v ^ { 2 }$