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

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...

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

The Cartesian coordinates of the point whose polar coordinates are $\left(\frac{1}{2}, 120^{\circ}\right)$ are:

Two fixed points are $A(a, 0)$ and $B(-a, 0)$. If $\angle A - \angle B = \theta$,then the locus of point $C$ of triangle $ABC$ will be

Let $ABCD$ be a square and $E$ be a point outside $ABCD$ such that $E, A, C$ are collinear in that order. Suppose $EB = ED = \sqrt{130}$ and the areas of $\triangle EAB$ and square $ABCD$ are equal. Then,the area of square $ABCD$ is