Write an equation for a circle if the endpoints of a diameter are at (–7, 1) and (5, 1).

The diameter is 12 units long. Their equation could be seen in y = 1, because it is a horizontal line. From x = - 7 to x = 0 is 7 units. From x = 0 to x = 5, is 5 units. 5 + 7 = 12. This means the radius is 6. We will use this later. If you need another way to find the radius, let me know. I can just use distance formula. 

We will use these endpoints to find the center. 

Midpoint = 
= 
= 
= (- 1, 1)

This is the center. 

The equation of a circle is (x - h)² + (y - k)² = radius² where (h, k) is the center. 

Plug in our given information now.

(x + 1)² + (y - 1)² = 6²

(x + 1)² + (y - 1)² = 36 is your equation.