Answer:
The equation for the circle is (x-0)^2+(y+3)^2=25
Explanation:
The radius is half the diameter. To find the length of the diameter we need to calculate the distance that (3,1) is to (-3,-7) which is sqrt(6^2+8^2)=10 .
The radius is therefore 10/2=5.
We also need the center of the circle (the midpoint of a diameter is the center of a circle). So we just need to average the x's and y's to find the midpoint between (3,1) and (-3,-7) which is (0,-3).
The equation for the circle is (x-0)^2+(y+3)^2=25
I just plugged my info into (x-h)^2+(y-k)^2=r^2
where (h,k) is center and r is radius