Write the Appropriate Rotation Formulas So That in a Rotated $$4 x ^ { 2 } + 5 x y + 4 y ^ { 2 } - 8 x + 8 y = 0$$

question 105

Multiple Choice

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term.
- $$4 x ^ { 2 } + 5 x y + 4 y ^ { 2 } - 8 x + 8 y = 0$$

• A) \(x = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } - y ^ { \prime } \right) ; y = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } + y ^ { \prime } \right)\)
• B) \(x = - y ^ { \prime } ; y = x ^ { \prime }\)
• C) \(x = \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } x ^ { \prime } - \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } y ^ { \prime } ; y = \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } x ^ { \prime } + \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } y ^ { \prime }\)
• D) \(x = \frac { 1 } { 2 } x ^ { \prime } - \frac { \sqrt { 3 } } { 2 } y ^ { \prime } ; y = \frac { \sqrt { 3 } } { 2 } x ^ { \prime } + \frac { 1 } { 2 } y ^ { \prime }\)

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