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