$A(2,3), B(-1,1)$ 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

The circle $x^2+y^2-8 x-12 y+\alpha=0$ lies in the first quadrant without touching the coordinate axes. If $(6,6)$ is an interior point to the circle, then

The equation of the circle whose diameter is the common chord of the circles $x^2+y^2-6 x-7=0$ and $x^2+y^2-10 x+16=0$ is