Question

The equation of circle having a diameter with endpoints (-2, 1) and (6, 7) is

(x - 4)² + (y - 3)² = 25
(x - 2)² + (y - 4)² = 25
(x - 2)² + (y - 4)² = 100

Answer 1

`(x-2)^(2)+(y-4)^(2)=25`

Explanation:

In the picture you can see that
`(x-2)^(2)+(y-4)^(2)=25` has endpoints of (-2, 1) and (6, 7)

Answer 2

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.