The locus of the point of intersection of perpendicular tangents to the circle $x^{2}+y^{2}=16$ is

Let $S = 0$ be the locus of the center of a variable circle which intersects the circle $x^2 + y^2 - 4x - 6y = 0$ orthogonally at the point $(4, 6)$. If $P$ is a variable point on $S = 0$,then the least value of $OP$ is (where $O$ is the origin).

If a circle $S$ passing through the point $(3,4)$ cuts the circle $x^2+y^2=36$ orthogonally,then the locus of the centre of $S$ is

If one end of the diameter is $(1, 1)$ and the other end lies on the line $x+y=3$,then the locus of the centre of the circle is

If $A (c, 0)$ and $B (-c, 0)$ are two points,find the locus of point $P$ such that $PA^{2} + PB^{2} = AB^{2}$.

The locus of the moving point $P$,such that $2PA = 3PB$ where $A$ is $(0,0)$ and $B$ is $(4,-3)$,is