The locus of the point $P$ which is equidistant from $3x + 4y + 5 = 0$ and $9x + 12y + 7 = 0$ is:

$A$ line passing through the point $(1, 2)$ meets the axes at $P$ and $Q$ such that it forms a triangle $OPQ$,where $O$ is the origin. If the area of triangle $OPQ$ is minimum,then the slope of the line $PQ$ is:

If the sum of the distances of a point from two perpendicular lines in a plane is $1$,find its locus.

The ends of a rod of length $l$ move on two mutually perpendicular lines. The locus of the point on the rod which divides it in the ratio $1 : 2$ is

If $A=(-1, 2)$ and $B=(1, -2)$ are two points and $P$ is a variable point such that the area of $\triangle PAB$ is always $1$,then the equation of the locus of $P$ is

$A$ line is drawn through the point $(1, 2)$ to meet the coordinate axes at $P$ and $Q$ such that it forms a $\triangle OPQ$,where $O$ is the origin. If the area of $\triangle OPQ$ is least,then the slope of the line $PQ$ is