The points $(-a, -b)$,$(0, 0)$,$(a, b)$,and $(a^2, ab)$ are

The point to which the origin is to be shifted to eliminate $x$ and $y$ terms of the equation $4x^2+9y^2-8x+36y+4=0$ is

If the polar coordinates of a point are $\left( \sqrt{2}, -\frac{3\pi}{4} \right)$,what are its Cartesian coordinates?

Point $A(5, 12)$ is rotated about the origin $O$ in the $XY$-plane through an angle of $30^\circ$ in the anticlockwise direction to a new position $B$. The ordinate of point $B$ is...

If a square $ABCD$,where $A(0,0), B(2,0), C(2,2)$ and $D(0,2)$ undergoes the following transformations successively,then the final figure would be a:
$(i)$ $f_1(x, y) \longrightarrow (y, x)$
(ii) $f_2(x, y) \longrightarrow (x+3y, y)$
(iii) $f_3(x, y) \longrightarrow \left(\frac{x-y}{2}, \frac{x+y}{2}\right)$

If the Cartesian coordinates of a point are $\left(\frac{-5 \sqrt{3}}{2}, \frac{5}{2}\right)$,then its polar coordinates are