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

Let $A(2, 3)$ and $B(-4, 5)$ be two fixed points. If a point $P(x, y)$ moves such that the area of $\Delta PAB = 12$ square units,find the locus of $P$.

If the algebraic sum of the perpendicular distances from the points $(2,0)$,$(0,2)$,and $(1,1)$ to a variable line is zero,then the variable line always passes through a fixed point. The coordinates of that point are

$A(-4,0)$ and $B(4,0)$ are two fixed points. $C$ and $D$ are two points on the $Y$-axis such that $CD=4$ and $C$ is a point below $D$. Then the locus of the point of intersection of the lines $AC$ and $BD$ is

The locus of the mid-point of the segment intercepted between the axes by the variable line $x \cos \alpha + y \sin \alpha = p$,where $p$ is a constant,is

$ABC$ is an isosceles triangle. If the coordinates of the base are $(1, 3)$ and $(-2, 7)$,then the coordinates of vertex $A$ can be: