When the axes are rotated through an angle `pi//6`. Find the transformed equation of `x^2+2sqrt3xy-y^2=2a^2`.

When the axes rotated through an angegle (pi)/(4) , find the transformed equation of 3x^2+10xy+3y^2=9 .

When the origin is shifted to (-2,-3) and the axes are rotated through an angle 45^(0) , find the transformed equation of 2x^(2)+4xy-5y^(2)+20x-22y-14 = 0 .

When the axes are rotated through an angle 45^@ , the transformed equation of a curve is 17x^2-16xy+17y^2=225 . Find the original equation of the curve.

If the coordinate axes are rotated through an angle (pi)/(6) about the origin, then transformed equation of sqrt(3)x^2-4xy+sqrt(3)y^2=0 is

If the corrdinate axes are rotated through an angle (pi)/(6) about the origin, then the transformed equation of sqrt(3)x^(2) - 4xy + sqrt(3)y^(2) = 0 is