Use Axis of Rotation Formulas for X and Y to Transform

question 14

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) \(\frac { 3 \mathrm { u } ^ { 2 } } { 16 } + \frac { \mathrm { v } ^ { 2 } } { 16 } = 1\)

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