JEE MATHEMATICS MCQ: TRANSFORMATION OF AXES

1 Easy

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Analyzing +4 | -1

Let

0 \le \theta \le \frac{\pi }{2}

and

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

such that

{x^2} + 4xy + {y^2} = a{X^2} + b{Y^2},

, where

a,b

are constants, then

View answer and explanation

Correct option: C

a = 3,\;b = - 1,\;\theta = \frac{\pi }{4}

Option C (

a = 3,\;b = - 1,\;\theta = \frac{\pi }{4}

) is correct because substituting these values into the given equation satisfies the condition.

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