Answer
$(x-5)^2+(y-\frac{9}{2})^2=\frac{169}{4}$
Work Step by Step
Step 1. Given two endpoints $(-1,2),(11,7)$ of a diameter, we can find the midpoint (center of the circle) as $(\frac{-1+11}{2},\frac{2+7}{2})$ or $(5,\frac{9}{2})$
Step 2. The radius can be found as $2r=\sqrt {(-1-11)^2+(2-7)^2}=13$, thus $r=\frac{13}{2}$
Step 3. We can write the equation of the circle as $(x-5)^2+(y-\frac{9}{2})^2=\frac{169}{4}$
