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Suppose the new axes X, Y are generated by rotating the coordinate axes x, y about the origin through an angle of `30^(@)` in the anti-clockwise direction. Then the transformed equation of `x^(2)+2sqrt(3) xy-y^(2)=2a^(2)` with respect to new axes X, Y is

A

`X^(2)-Y^(2)=a^(2)`

B

`X^(2)+y^(2)=2a^(2)`

C

`X^(2)+2 sqrt(3) XY-Y^(2) =2a^(2)`

D

`X^(2)-Y^(2)=2a^(2)`

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A
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