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

The coordinates of the points $O$,$A$,and $B$ are $(0,0)$,$(0,4)$,and $(6,0)$ respectively. If a point $P$ moves such that the area of $\Delta POA$ is always twice the area of $\Delta POB$,then the equation to both parts of the locus of $P$ is

The coordinates of a point $P$ on the line $2x - y + 5 = 0$ such that $|PA - PB|$ is maximum,where $A$ is $(4, -2)$ and $B$ is $(2, -4)$,are:

The equation of the locus of a point which is equidistant from the points $(2, 3)$ and $(4, 5)$ is

Two families of lines are given by $ax + by + c = 0$ and $4a^2 + 9b^2 - c^2 - 12ab = 0$. Then the line common to both the families is

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