If the origin is shifted to the point $(2, -5)$ and the axes are kept parallel,what will be the new coordinates of the point $(-5, 3)$?

The coordinates of the point $(3,-7,5)$ in the new system,when the origin is shifted to the point $(-1,-1,-1)$ by the translation of axes,are

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

If the origin is shifted to a point $(h, k)$ by translation of axes in order to make the equation $x^2+5xy+2y^2+5x+6y+7=0$ free from first-order terms,then:

The transformed equation of $3x^2 - 4xy = r^2$ when the coordinate axes are rotated through an angle $\tan^{-1}(2)$ is:

The coordinate axes are rotated through an angle $135^{\circ}$. If the coordinates of a point $P$ in the new system are known to be $(4, -3)$,then the coordinates of $P$ in the original system are