If the axes are rotated through, an angle `theta`, the transformed equation of `x^(2) + y^(2)=25` is

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 .

If the axes are rotated through an angle 30^(0) about the origin then the transformed equation of x^(2) + 2 sqrt(3) xy - y^(2) = 2a^(2) is

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