I am new to this answers forum, and there seem to be limited tools for which I can use to write, but I'll try my best.
First you need the Standard Form of the Equation of a Circle:
(x-h)^{2 }+ (y-k)^{2} = r^{2}
First you want to find the distance between the two endpoints, which will give you your
Diameter, using the Distance Formula. Then divide that answer by two to get your
Radius which you will plug directly into your Equation of a Circle.
The (h,k) is the Center Point of your circle. You can find this with with
Midpoint Formula using the two endpoints given in the problem.
I solved this problem using the steps above and I got the answer:
(x-13.5)^{2}+(y-15.5)^{2} = (14.3)^{2}
Normally you would leave the h and k as fractions, but I was having trouble figuring out how to format it properly.
Also if there is anything I missed, you disagree with, or something I did not explain fully, please tell me.