The general form of the equation of a circle is (x-h)^2+(y-k)^2=r^2(x−h)2+(y−k)2=r2 where (h,k)(h,k) are the coordinates of the center and rr is the length of the radius.
We are given that the center is at (2,6)(2,6) so we need to figure out the length of the radius. Since we know the circle passes through the point (3,1)(3,1), we know the radius is just the distance between (2,6)(2,6) and (3,1)(3,1). In the equation, we end up using r^2r2 instead of rr which makes our calculations a bit easier:
"Distance"=r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)Distance=r=√(x2−x1)2+(y2−y1)2
r^2=(x_2-x_1)^2+(y_2-y_1)^2r2=(x2−x1)2+(y2−y1)2
r^2=(2-3)^2+(6-1)^2r2=(2−3)2+(6−1)2
r^2=26r2=26
Now that we have everything, we just substitute our values into the equation of a circle: (x-2)^2+(y-6)^2=26(x−2)2+(y−6)2=26
