Answer
$(x-1)^2+(y+\frac{13}{2})^2=\frac{85}{4}$
Work Step by Step
The middlepoint between $(-2,-3)$ and $(4,-10)$ is the center of the circle:
$\frac{(-2,-3)+(4,-10)}{2}=(1,-\frac{13}{2})$, that is: $h=1$, $k=-\frac{13}{2}$
The distance from the center to an endpoint is the radius:
$r=\sqrt {[1-(-2)]^2+[-\frac{13}{2}-(-3)]^2}=\sqrt {9+\frac{49}{4}}=\frac{\sqrt {85}}{2}$
Equation of a circle:
$(x−h)^2+(y−k)^2=r^2$ (standard form)
$(x-1)^2+[y-(-\frac{13}{2})]^2=(\frac{\sqrt {85}}{2})^2$
$(x-1)^2+(y+\frac{13}{2})^2=\frac{85}{4}$
