If the sum of the distances of a point $P(x, y)$ from two perpendicular lines in a plane is $1$,then the locus of $P$ is a

$A$ light ray emerging from the point source placed at $P(1, 3)$ is reflected at a point $Q$ on the $x$-axis. If the reflected ray passes through the point $R(6, 7)$,then the abscissa of $Q$ is

$A$ variable straight line passes through the point of intersection of the lines $x + 2y = 1$ and $2x - y = 1$ and meets the coordinate axes at $A$ and $B$. The locus of the midpoint of $AB$ is:

Let $P$ be a moving point such that the sum of its perpendicular distances from the lines $2x + y - 3 = 0$ and $x - 2y + 1 = 0$ is always $2 \, units$. Then,the area bounded by the locus of point $P$ is:

Every point $(x, y)$ on the curve $3x + 2y - 3xy = 0$ is the centroid of a triangle formed by the coordinate axes and a line $(L)$ intersecting both the coordinate axes. Then all such lines $(L)$

If a straight line drawn through the point of intersection of the lines $4x + 3y - 1 = 0$ and $3x + 4y - 1 = 0$ meets the coordinate axes at the points $P$ and $Q$,then the locus of the midpoint of $PQ$ is: