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