$A$ ray of light passing through the point $A(1, 2)$ is reflected at a point $B$ on the $x$-axis and then passes through $(5, 3)$. Then the equation of $AB$ is:

$A(2,0), B(0,2), C(-2,0)$ are three points. Let $a, b, c$ be the perpendicular distances from a variable point $P(x, y)$ onto the lines $AB, BC$ and $CA$ respectively. If $a, b, c$ are in arithmetic progression,then the locus of $P$ is

Let $A(2,3), B(3,-6), C(5,-7)$ be three points. If $P$ is a point satisfying the condition $PA^2+PB^2=2PC^2$,then a point that lies on the locus of $P$ is

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

Suppose that the three points $A, B$ and $C$ in the plane are such that their $x$-coordinates as well as $y$-coordinates are in $GP$ with the same common ratio. Then,the points $A, B$ and $C$

The line $AB$ cuts off equal intercepts $2a$ from the axes. From any point $P$ on the line $AB$,perpendiculars $PR$ and $PS$ are drawn to the axes. The locus of the mid-point of $RS$ is