JEE MATHEMATICS MCQ: TRANSFORMATION OF AXES

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Analyzing +4 | -1

x = X\cos \theta - Y\sin \theta ,y = X\sin \theta + Y\cos \theta

and

{x^2} + 4xy + {y^2} = A{X^2} + B{Y^2},0 \le \theta \le \frac{\pi }{2},

then

View answer and explanation

Correct option: B

\theta = \frac{\pi }{4}

Option B (

\theta = \frac{\pi }{4}

) is correct because substituting the given transformations into the equation and comparing coefficients leads to the condition that

\theta = \frac{\pi}{4}

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