Question 776·Medium·Math

The endpoints are the ends of a diameter, so their midpoint, the point halfway between them, is the circle's center. Type $P=(-2,3)$ and $Q=(6,-1)$, then $\operatorname{midpoint}(P,Q)$. Click the plotted midpoint; Desmos shows $(2,1)$.

The distance from $P$ to $Q$ is the whole diameter, not the radius. Halve that distance before squaring to get $r^2$. Type $\left(\operatorname{distance}(P,Q)/2\right)^2$. Desmos prints $20$, so $r^2=20$. The $80$ in two choices is the squared diameter, which would make the circle too large.

In standard form, $(x-h)^2+(y-k)^2=r^2$, the center is $(h,k)$. Use the center $(2,1)$ and $r^2=20$:

The signs inside the parentheses are opposite the center coordinates. This equation represents the circle with diameter $\overline{PQ}$. Choice D.