Answer
$(x-7)^2+(y-5)^2=116$
Work Step by Step
The middlepoint between $(11,-5)$ and $(3,15)$ is the center of the circle:
$\frac{(11,-5)+(3,15)}{2}=(7,5)$, that is: $h=7$, $k=5$
The distance from the center to an endpoint is the radius:
$r=\sqrt {(7-11)^2+[5-(-5)]^2}=\sqrt {16+100}=\sqrt {116}$
Equation of a circle:
$(x−h)^2+(y−k)^2=r^2$ (standard form)
$(x-7)^2+(y-5)^2=(\sqrt {116})^2$
$(x-7)^2+(y-5)^2=116$
