Determine the Appropriate Rotation Formulas to Use So That the New

question 106

Short Answer

Determine the appropriate rotation formulas to use so that the new equation contains no xy-term.
- $11 x ^ { 2 } - 4 x y + 7 y ^ { 2 } - 8 x + 8 y = 0$
A) $x = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } - y ^ { \prime } \right)$ and $y = \frac { \sqrt { 2 } } { 2 } \left( x ^ { \prime } + y ^ { \prime } \right)$
B) $x = \frac { 1 } { 2 } x ^ { \prime } - \frac { \sqrt { 3 } } { 2 } y ^ { \prime }$ and $y = \frac { \sqrt { 3 } } { 2 } x ^ { \prime } + \frac { 1 } { 2 } y ^ { \prime }$
C) $x = - y ^ { \prime }$ and $y = x ^ { \prime }$
D) $x = \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } x ^ { \prime } - \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } y ^ { \prime }$ and $y = \frac { \sqrt { 2 + \sqrt { 2 } } } { 2 } x ^ { \prime } + \frac { \sqrt { 2 - \sqrt { 2 } } } { 2 } y ^ { \prime }$

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

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