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If the hyperbola x^2-y^2=4 is rotated by...

If the hyperbola `x^2-y^2=4` is rotated by `45^0` in the anticlockwise direction about its center keeping the axis intact, then the equation of the hyperbola is `x y=a^2,` where `a^2` is equal to___________

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The correct Answer is:
3
(a,2) lies on director cirector circle `x^(2)+y^(2)=7`. Therefore `a^(2)=3`.
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