If the point $(x, y)$ is equidistant from the points $(a + b, b - a)$ and $(a - b, a + b)$,then:

If $2a + b + 3c = 0$,then the line $ax + by + c = 0$ passes through the fixed point that is

If $L : ax + by + c = 0$ is a variable straight line,where $a, b$ and $c$ are the second,fourth,and seventh terms of an $AP$ respectively,then $L$ passes through the fixed point:

Let $A(2, -3)$ and $B(-2, 1)$ be two vertices of $\Delta ABC$. If the centroid of the triangle moves on the line $2x + 3y = 1$, then the locus of the vertex $C$ is given by

$A$ point moves in the $xy$-plane such that the sum of its distances from two mutually perpendicular lines is always equal to $5$ units. The area (in sq units) enclosed by the locus of the point is

$A$ variable line passes through a fixed point $(a, b)$ and meets the coordinate axes at $A$ and $B$. The locus of the point of intersection of lines passing through $A$ and $B$ and parallel to the coordinate axes is: