The standard form equation of a circle with radius r is:

(x−h)^2+(y−k)^2=r^2,

where r is the radius, h and k are the coordinates of the center of the circle C(h, k).

The center of the circle is the midpoint of the line segment making the diameter AB, where A(2,3) and B(2,9). The midpoint formula is used to find the coordinates of the center C of the circle.

h coordinate of C = (2 + 2) / 2 = 2

k coordinate of C = (3 + 9) / 2 = 6

The radius r is half the distance between A and B.

r = (1/2) ([2 - 2]2 + [9 - 3]2 )1/2

r = 3

h = 2

k = 6

The standard form of the equation of this circle is:

(x - 2)^2 + (y - 6)^2 = 3^2