Answer
$(x+2)^2+(y+1)^2=41$
Work Step by Step
Step 1. Given two endpoints $(3,-5),(-7,3)$ of a diameter, we can find the midpoint (center of the circle) as $(\frac{3-7}{2},\frac{-5+3}{2})$ or $(-2, -1)$
Step 2. The radius can be found as $r=\sqrt {(-2-3)^2+(-1-(-5))^2}=\sqrt {41}$
Step 3. We can write the equation of the circle as $(x+2)^2+(y+1)^2=41$
