If the axes are rotated through an angle $30^{\circ}$ about the origin, then the tranformed equation of $x^2 + 2 \sqrt{3} xy - y^2 = 2a^2$, is :

Question

( A ) $x^2 - y^2 = 2a^2$
( B ) $x^2 - y^2 = a^2$
( C ) $x^2 + y^2 = a^2$
( D ) $x^2 + y^2 = 2a^2$