The points A and B have coordinates (5, -1) and (13, 11) respectively - Edexcel - A-Level Maths Pure - Question 3 - 2005 - Paper 2

Since AB is a diameter of circle C, the center of the circle is the mid-point of AB, which we calculated earlier as (9, 5). The radius can be found by calculating the distance from the center to either point A or point B.

Using the distance formula:

$r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Choosing point A(5, -1):

$r = \sqrt{(9 - 5)^2 + (5 - (-1))^2} = \sqrt{(4)^2 + (6)^2} = \sqrt{16 + 36} = \sqrt{52}$

The equation of the circle in standard form is given by:

$(x - h)^2 + (y - k)^2 = r^2$

Where (h, k) is the center and r is the radius. Thus, substituting our values gives:

$(x - 9)^2 + (y - 5)^2 = 52$

This is the equation for circle C.