$A$ variable line $\frac{x}{a}+\frac{y}{b}=1$ is such that $a+b=4$. The locus of the midpoint of the portion of the line intercepted between the axes is

Through a given point $P(a, b)$,a straight line is drawn to meet the axes at $Q$ and $R$. If the parallelogram $OQSR$ is completed,then the equation of the locus of $S$ is (given $O$ is the origin):

$A$ point $P$ on a line is at a distance of $4$ units from the origin $(0,0)$. If the line makes an angle of $60^{\circ}$ with the negative direction of the $X$-axis,then the coordinates of $P$ are

The Cartesian form of the polar equation $\theta = \tan^{-1} 2$ is

Suppose we have to cover the $XY$-plane with identical tiles such that no two tiles overlap and no gap is left between the tiles. Suppose that we can choose tiles of the following shapes: equilateral triangle,square,regular pentagon,regular hexagon. Then,the tiling can be done with tiles of

$A$ light ray emerging from a point source at $A(2,3)$ is reflected on the $Y$-axis at point $B$ and passes through point $C(5,10)$. Then the coordinates of $B$ are: