Question

the endpoints of the diameter of a circle are (−6, 6) and (6, −2), what is the standard form equation of the circle?

Answer 1

The equation of a circle in standard form is


`(x - h)^2 + (y - k)^2 = r^2`

where (h, k) is the center of the circle, and r is the radius if the circle.

We need to find the radius and center of the circle.
We are given a diameter, so to find the center, we need the midpoint of the diameter.

M = ((-6 + 6)/2, (6 + (-2))/2) = (0, 2)
The center is (0, 2).

To find the radius, we find the length of the given diameter and divided by 2.


`d = √((-6 - 6)^2 + (6 - (-2))^2))`


`d = √(144 + 64)`


`d = √(208)`


`r = (d)/(2) = (√(208))/(2) = (√(208))/(√(4)) = √(52)`


`(x - 0)^2 + (y - 2)^2 = (√(52))^2`


`x^2 + (y - 2)^2 = 52`