Rotate the Axes to Eliminate The $x y$ -Term in the Equation

question 112

Multiple Choice

Rotate the axes to eliminate the $x y$ -term in the equation. Then write the equation in standard form.
$41 x ^ { 2 } + 18 x y + 41 y ^ { 2 } - 800 = 0$

• A) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 25 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1\)
• B) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 9 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 16 } = 1\)
• C) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 16 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 36 } = 1\)
• D) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 9 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 25 } = 1\)
• E) \(\frac { \left( x ^ { \prime } \right) ^ { 2 } } { 16 } + \frac { \left( y ^ { \prime } \right) ^ { 2 } } { 25 } = 1\)

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