Hello sally1,
 The equation for a circle is: (x-h)2 + (y-k)2 = r2 
 (h, k) is the center.
 So the center of the circle will be halfway between the endpoints of the diameter (the midpoint). Use the Midpoint Formula: [(x1+x2)/2 ,  (y1+y2)/2]
 = [(-1 + 5)/2 , (1 + 9)/2]
 = (2, 5)
 So the equation so far is: (x-2)2 + (y-5)2 = r2
 Now find the radius, which is the diameter divided in half. 
 Use the Distance Formula to find the diameter: 
 Plug in the endpoints of the diameter: d = sqrt[(5 - -1)2 + (9- 1)2]
 Simplify.
 d = sqrt( 36 + 64)
 d = sqrt(100)
 d = 10
 Half of that = radius = 5
 Radius squared = 25
 So the final equation: (x-2)2 + (y-5)2 = 25