If $(3,-2)$ is the centre of the circle $S \equiv x^2+y^2+2 g x+2 f y-23=0$ and $A$ is a point on the circle $S=0$ such that its distance from a point $P(-1,-5)$ is least, then $A=$

Two circles which touch both the coordinate axes intersect at the points $A$ and $B$. If $A=(1,2)$, then $A B=$

The lines $4 x-3 y+2=0$ intersects the circle $x^2+y^2-2 x+6 y+c=0$ at two points $A, B$ and $A B=8$. If $(1, k)$ is a point on the given circle and $k>0$, then $k=$

If $2 x-3 y+5=0$ and $4 x-5 y+7=0$ are the equations of the normals drawn to a circle and $(2,5)$ is a point on the given circle, then the radius of the circle is