If the axes are shifted to `(-2,-3)` and rotated through `pi/4` then transformed equation of `2x^2 + 4xy - 5y^2 + 20x - 22y - 14 = 0` 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 origin is shifted to (2,3) and the axes are rotated through an angle 45^(@) about that point, then the transformed equation of 2x^(2) + 2y^(2) - 8x - 12y + 18 = 0 is

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 .

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