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.
- $7 x ^ { 2 } + 6 \sqrt { 3 } x y + 13 y ^ { 2 } = 57$

A) $\frac { 16 u ^ { 2 } } { 57 } + \frac { 4 v ^ { 2 } } { 57 } = 1$
B) $\mathrm { v } = \frac { \mathrm { u } ^ { 2 } } { 4 }$
C) $\frac { 4 u ^ { 2 } } { 57 } + \frac { 16 v ^ { 2 } } { 57 } = 1$
D) $\frac { 3 \mathrm { u } ^ { 2 } } { 114 } + \frac { \mathrm { v } ^ { 2 } } { 114 } = 1$