The locus of a point which is at a distance of $4$ units from $(3, -2)$ in the $xy$-plane is

$A$ circle of constant radius $a$ passes through the origin $O$ and cuts the coordinate axes at points $P$ and $Q$. The equation of the locus of the foot of the perpendicular from $O$ to $PQ$ is:

From a point $A(0,3)$ on the circle $(x+2)^2+(y-3)^2=4$,a chord $AB$ is drawn and it is extended to a point $Q$ such that $AQ=2AB$. Then the locus of $Q$ is

$A$ rod $PQ$ of length $2a$ moves with its ends on the coordinate axes. Find the locus of the circumcenter of $\Delta OPQ$.

Let $A = (a, 0)$ and $B = (-a, 0)$ be two fixed points. For $a \in (-\infty, 0)$,point $P$ moves in the plane such that $PA = nPB$ $(n \neq 0, n \neq 1)$. If $n > 1$,then which of the following is true regarding the positions of $A$ and $B$ with respect to the locus of $P$?

If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B,$ then the locus of the foot of the perpendicular from $O$ on $AB$ is