What is the equation of this circle in standard form?

The standard equation of a circle of radius r with center at (h,k) is:

(x-h)^2 + (y-k)^2 = r^2.  The two points (2,4) and (9,4) are on this circle.  According to the diagram, the diameter of the circle is 9-2, or 7, which means that the radius is 7/2.    Where is the center?  Starting at M(2,4), and moving 7/2 units to the right will bring us to the center.  So the center is (2+7/2, 4), or
(11/2, 4).  Let's put this data to use:

(x - 11/2)^2 + (y - 4)^2 = (7/2)^2  =  49/4.  This is the simplest form of the equation of this circle.