The points A and B have coordinates (5, -1) and (13, 11) respectively - Edexcel - A-Level Maths Pure - Question 4 - 2005 - Paper 2

Since AB is the diameter of circle C, the center of the circle is the mid-point of AB which we found to be (9, 5). The radius is the distance from the center to either endpoint A or B.

Calculating the radius (r):

Using point A(5, -1):

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

Now, the equation of the circle can be written as:

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

Substituting for r:

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

So, the equation for circle C is:

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