The midpoint of the diameter endpoints is the center of the circle...
((2+9)/2, (4+4)/2)
(5.5, 4) is the center of the circle...
The distance between the two endpoints is the diameter of the circle...
d^2=(4-4)^2+(9-2)^2
d^2=0+49
d^2=49
d=7
So the radius is d/2 which is 3.5
Now the equation of a circle is:
(x-h)^2+(y-k)^2=r^2 where (h,k) is the coordinates of the center and r is the radius.
Earlier we found (h,k) to be (5.5, 4) and r=3.5 so our equation is:
(x-5.5)^2+(y-4)^2=3.5^2
(x-5.5)^2+(y-4)^2=12.25