If a direct common tangent drawn to the circle $x^2+y^2-6 x+4 y+9=0$ and $x^2+y^2+2 x-2 y+1=0$ touches the circles at $A$ and $B$, then $A B=$

$A(2,3), B(-1,1)$ are two points. If $P$ is a variable point such that $\angle A P B=90^{\circ}$, then locus of $P$ is

The largest among the distances from the point $P(15,9)$ to the points on the circle $x^2+y^2-6 x-8 y-11=0$ is