Write the Appropriate Rotation Formulas So That in a Rotated $$6 x ^ { 2 } - 4 x y + 3 y ^ { 2 } - 8 x + 8 y = 0$$

question 135

Multiple Choice

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term.
- $$6 x ^ { 2 } - 4 x y + 3 y ^ { 2 } - 8 x + 8 y = 0$$

• A) \(x = \sqrt { 5 } \left( \frac { x ^ { \prime } - 2 y ^ { \prime } } { 5 } \right) ; y = \sqrt { 5 } \left( \frac { 2 x ^ { \prime } + y ^ { \prime } } { 5 } \right)\)
• B) \(x = \sqrt { 5 } \left( \frac { 2 x ^ { \prime } - y ^ { \prime } } { 5 } \right) ; y = \sqrt { 5 } \left( \frac { x ^ { \prime } + 2 y ^ { \prime } } { 5 } \right)\)
• C) \(x = \frac { 3 } { 5 } x ^ { \prime } - \frac { 4 } { 5 } y ^ { \prime } ; y = \frac { 4 } { 5 } x ^ { \prime } + \frac { 3 } { 5 } y ^ { \prime }\)
• D) \(x = \frac { 7 } { 25 } x ^ { \prime } - \frac { 24 } { 25 } y ^ { \prime } ; y = \frac { 24 } { 25 } x ^ { \prime } + \frac { 7 } { 25 } y ^ { \prime }\)

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Definitions:

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