The center of the circle is the midpoint of the diameter.
The 'x' coordinate of the midpoint is (1/2) (6 - 2) = 2 The 'y' coordinate of the midpoint is (1/2) (7 + 1) = 4 The center of the circle is the point (2, 4) .
The length of the diameter of the circle is the distance between the endpoints of the diameter.
The distance between (-2, 1) and (6, 7) is
√ (8² + 6²)
= √ (64 + 36)
= √ 100 = 10 .
The radius of the circle is 1/2 of 10 = 5 .
Now, the equation of any circle is
(x - [x of the center])² + (y - [y of the center])² = (radius)² .
and we have all the numbers now.
(x - 2)² + (y - 4)² = (5)² .
I'm very happy to see that this equation is actually one of the choices ! I'll bet you are too.
