The equation of a circle is (x - h) ** 2 + (y - k)**2 = r**2, where (h,k) is the coordinates of the center of the circle, (x,y) are the coordinates of any point on the circle and r is the radius of the circle.
We are given the center (h,k) = (2,3), so now we have (x-2)**2 + (y-3)**2 = r**2.
To complete the equation we need to compute the value of r.
We are given a point (4,6) on the circle, so we can plug x=4 and y=6 into our equation to get r**2
(4-2)**2 + (6-3)**2 = r**2, so that r*2 = 2**2 + 3**2 = 13.
So our equation become (x-2)**2 + (y-3)**2 = 13
We also could have computed this by using the distance formula to find the distance between (2,3) and (4,6) since the distance between the center and any point on the circle is the radius:
(6-3)**2 + (4-2)**2 = r**2.
