Write the Appropriate Rotation Formulas So That in a Rotated $$14 x ^ { 2 } - 24 x y + 7 y ^ { 2 } + 30 x - 40 y - 45 = 0$$

question 205

Multiple Choice

Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term.
- $$14 x ^ { 2 } - 24 x y + 7 y ^ { 2 } + 30 x - 40 y - 45 = 0$$

• A) \(x = \frac { 3 } { 5 } x ^ { \prime } - \frac { 4 } { 5 } y ^ { \prime } ; y = \frac { 4 } { 5 } x ^ { \prime } + \frac { 3 } { 5 } y ^ { \prime }\)
• B) \(x = \frac { 7 } { 25 } x ^ { \prime } - \frac { 24 } { 25 } y ^ { \prime } ; y = \frac { 24 } { 25 } x ^ { \prime } + \frac { 7 } { 25 } y ^ { \prime }\)
• C) \(x = \frac { 89 } { 100 } x ^ { \prime } - \frac { 9 } { 20 } y ^ { \prime } ; y = \frac { 9 } { 20 } x ^ { \prime } + \frac { 89 } { 100 } y ^ { \prime }\)
• 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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