Answer
$(x-1)^2+(y-\frac{5}{2})^2=\frac{289}{4}$
Work Step by Step
Step 1. Given two endpoints $(-3,10),(5,-5)$ of a diameter, we can find the midpoint (center of the circle) as $(\frac{-3+5}{2},\frac{10-5}{2})$ or $(1,\frac{5}{2})$
Step 2. The radius can be found as $2r=\sqrt {(-3-5)^2+(10-(-5))^2}=17$, thus $r=\frac{17}{2}$
Step 3. We can write the equation of the circle as $(x-1)^2+(y-\frac{5}{2})^2=\frac{289}{4}$
