Question

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

Answer 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 = $( \frac{X1+X2}{2} , \frac{Y1+Y2}{2} )$
= $( \frac{- 7 + 5}{2} , \frac{1 + 1}{2} )$
= $( \frac{-2}{2} , \frac{2}{2} )$
= (- 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.