If $A(2,-3)$ and $B(-2,1)$ are two vertices of a triangle and the third vertex moves on the line $2x + 3y = 9$,then the locus of the centroid of the triangle is

If a variable straight line passing through the point of intersection of the lines $x-2y+3=0$ and $2x-y-1=0$ intersects the $X, Y$-axes at $A$ and $B$ respectively,then the equation of the locus of a point which divides the segment $AB$ in the ratio $-2:3$ is

The point whose abscissa is equal to its ordinate and which is equidistant from the points $(1, 0)$ and $(0, 3)$ is

Suppose a point $P$ moves so that $BP^2 - AP^2 = 121$,where $A$ and $B$ are $(2, 5)$ and $(5, 11)$ respectively. Then the locus of $P$ is a straight line,whose slope is

$A$ rod of length $2l$ slides with its ends on two perpendicular lines. The locus of its mid-point is

Let the algebraic sum of the perpendicular distances from the points $A(2, 0)$,$B(0, 2)$,and $C(1, 1)$ to a variable line be zero. Then,all such lines: