Question

What is the equation of a circle with diameter AB that has endpoints a(0,0) and B(8,6)

Answer 1

The equation of the circle with diameter AB that has endpoints a(0,0) and B(8,6) is (x - 4)^2 + (y - 3)^2 = 25.

Step-by-step explanation:

The equation of a circle can be represented in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Given the endpoints A(0,0) and B(8,6), we can find the center of the circle by taking the average of the x-coordinates and the average of the y-coordinates.

The center of the circle is (4, 3) and the radius is the distance from the center to one of the endpoints, which is 5.

Therefore, the equation of the circle is (x - 4)^2 + (y - 3)^2 = 5^2.

Answer 2

(8-0)^2+(6-0)^2=10^2
r=10
(x-8)^2+(y-6)^2=100