Answer
$(x-1)^2+(y-1)^2=25$
Work Step by Step
Step 1. Given two endpoints $(5,4),(-3,-2)$ of a diameter, we can find the midpoint (center of the circle) as $(\frac{5-3}{2},\frac{4-2}{2})$ or $(1,1)$
Step 2. The radius can be found as $r=\sqrt {(1-5)^2+(1-4)^2}=5$
Step 3. We can write the equation of the circle as $(x-1)^2+(y-1)^2=25$
