The equation $2 x y = 9$ is transformed to $x^{2} - y^{2} = 9$ by rotating the axes through an angle $\frac{π}{4}$ . Is this statement true or false?

True

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False

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Solution

The correct option is A True
$2 (x c o s \frac{π}{4} - y s i n \frac{π}{4}) (x s i n \frac{π}{4} + y c o s \frac{π}{4}) = 9$
or $2. \frac{x - y}{\sqrt{2}} . \frac{x + y}{\sqrt{2}} = 0$ or $x^{2} - y^{2} = 9$

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