To which point should the origin be shifted in order to eliminate the first-degree terms ($x$ and $y$ terms) from the equation $4x^2 + 9y^2 - 8x + 36y + 4 = 0$?

The vertices of a figure are $(-2, 2), (-2, -1), (3, -1),$ and $(3, 2)$. This figure is a:

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

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

The point of intersection of the diagonals of a square is at the origin,and the coordinate axes are drawn along the diagonals. If the side length of the square is $a$,then which of the following is $NOT$ a vertex of the square?

An insect is resting on the graph paper at a point $A(3, 2)$. Now it starts moving towards the west direction and covers a distance of $4 \ units$,then it turns towards the south and covers a distance of $3 \ units$ to reach point $B$. The polar coordinates of point $B$ will be: