If the origin is shifted to the point $(-2, 1)$,what are the new coordinates of the point $(4, -5)$?

If the axes are rotated through an angle $45^{\circ}$ about the origin in an anticlockwise direction,then the transformed equation of $y^2=4ax$ is

When the origin is shifted to the point $\left(\frac{3}{2}, \frac{3}{2}\right)$ by the translation of coordinate axes,then the transformed equation of $32 x^2+8 x y+32 y^2-108 x-108 y+99=0$ is

The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle $36^{\circ}$ is

When the coordinate axes are rotated about the origin in the positive direction through an angle $\frac{\pi}{4}$,if the equation $49x^2+25y^2=1225$ is transformed to $px^2+qxy+ry^2=t$ and the $G.C.D$ of $p, q, r, t$ is $1$,then:

When the origin is shifted to $(-1, 2)$ by the translation of axes,the transformed equation of $x^2+y^2+2x-4y+1=0$ is