Question 460801
The distance between the two points is {{{sqrt((5-3)^2 + (-3-4)^2) = sqrt(2^2 + (-7)^2) = sqrt(4 + 49) = sqrt(53)}}}.  Hence the radius is {{{sqrt(53)/2}}}.  The center is the midpoint of the two endpoints:  (1/2, 4).  Then the standard equation of the circle is {{{(x-1/2)^2 + (y-4)^2 = 53/4}}}.