How the equation is transformed when origin is changed and axes is rotated ?

Find the transformed equations of the following when the origin is shifted to the point (1, 1) by a translation of axes : xy-y^2-x +y=0 .

Find the transformed equation of When the axes of rotated through 90^(0), find the transformed equation of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1

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 .

Find the transformed equation of 4xy-3x^(2) = a^(2) when the axes are rotated through an angle Tan^(-1) 2.

Find the transformed equation of the straight line 2x-3y+5=0 ,when the origin is shifted to the point (3,-1) after transiation of axes.

The transformed equation of x^(2) -y^(2)=a^(2) when the axes are rotated through an angle pi//4 in clockwise direction is