Final answer:
The equation of the circle is (x-13)^2 + (y-14)^2 = 9.
Step-by-step explanation:
The equation of a circle can be written in the form (x-h)^2 + (y-k)^2 = r^2, where (h,k) represents the center of the circle and r represents the radius. In this case, since the circle is tangent to the line x=13, the x-coordinate of the center will be 13 and the radius will be the distance from the center to the line x=13. Since the circle is tangent, this distance will be the same as the distance from the center to any point on the line. Therefore, the equation of the circle is (x-13)^2 + (y-14)^2 = (13-10)^2 + (14-14)^2 = 9 + 0 = 9.