The point to which the origin should be shifted so that the equation $y^2-6y-4x+13=0$ is transformed to the form $y^2+Ax=0$ is

The transformed equation $3x^2 + 3y^2 + 2xy = 2$,when the coordinate axes are rotated through an angle $45^{\circ}$,is

If the coordinate axes are rotated through an angle $\frac{\pi}{6}$ about the origin,then the transformed equation of $\sqrt{3} x^2-4 x y+\sqrt{3} y^2=0$ 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

By shifting the origin to the point $(h, 5)$ by the translation of coordinate axes,if the equation $y=x^3-9x^2+cx-d$ transforms to $Y=X^3$,then $\left(d-\frac{c}{h}\right)=$

Transforming to parallel axes through a point $(p, q)$, the equation $2x^2 + 3xy + 4y^2 + x + 18y + 25 = 0$ becomes $2x^2 + 3xy + 4y^2 = 1$. Then: