If $A, B$ are the points of contact of the tangents drawn from the point $(-3,1)$ to the circle $x^2+y^2-4 x+2 y-4=0$, then the equation of the circumcircle of the $\triangle P A B$ is

A circle $C$ passing through the point $(1,1)$ bisects the circumference of the circle $x^2+y^2-2 x=0$. If $C$ is orthogonal to the circle $x^2+y^2+2 y-3=0$, then the centre of the circle $C$ is

$P$ and $Q$ are the points of trisection of the line segment joining the points $(3,-7)$ and $(-5,3)$. If $P Q$ subtends right angle at a variable point $R$, then the locus of $R$ is

If $A(1,2), B(2,1)$ are two vertices of an acute angled triangle and $S(0,0)$ is its circumcenter, then the angle subtended by $A B$ at the third vertex is