When the origin is shifted to $(h, k)$ by translation of axes,the transformed equation of $x^2+2x+2y-7=0$ does not contain the $x$ term and the constant term. Then $(2h+k) =$

When the origin is shifted to the point $(2,3)$ and then the coordinate axes are rotated through an angle $\frac{\pi}{3}$ in the counter-clockwise sense,then the transformed equation of $3 x^2+2 x y+3 y^2-18 x-22 y+50=0$ is

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

If the origin of a coordinate system is shifted to $(-\sqrt{2}, \sqrt{2})$ and the coordinate system is rotated anti-clockwise through an angle $45^{\circ}$,then the point $P(1, -1)$ in the original system has new coordinates

$A$ line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the axes are rotated through a given angle $\theta$ keeping the origin fixed,this line $L$ has the intercepts $p$ and $q$. Then

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 $\left(d-\frac{c}{h}\right)=$