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

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

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

13.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.