The transformed equation of the curve $2x^2+y^2-3x+5y-8=0$ when the origin is translated to the point $(-1, 2)$ is

By shifting the origin to the point $(-1, 2)$ through translation of axes,if $ax^2+2hxy+by^2+2gx+2fy+c=0$ is the transformed equation of $2x^2-xy+y^2-3x+4y-5=0$,then $2(f+g+h)=$

To which point should the origin be shifted,without changing the direction of the axes,so that the equation $x^2 + y^2 - 4x + 6y - 7 = 0$ transforms into an equation that contains no first-degree terms?

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

The origin is translated to $(1,2)$. The point $(7,5)$ in the old system undergoes the following transformations successively.
$I$. Moves to the new point under the given translation of origin.
$II$. Translated through $2$ units along the negative direction of the new $X$-axis.
$III$. Rotated through an angle $\frac{\pi}{4}$ about the origin of the new system in the clockwise direction. The final position of the point $(7,5)$ is

The angle by which axes are to be rotated without changing the origin so that the transformed equation of $x^2+4xy-y^2=0$ in new coordinates $(X, Y)$ does not contain the $XY$ term is