Final answer:
The equation of a circle with diameter endpoints can be found using the midpoint formula to find the center and the distance formula to find the radius.
Step-by-step explanation:
The equation of a circle with diameter endpoints can be found using the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula:
(x, y) = ((x1 + x2)/2, (y1 + y2)/2)
For a circle with diameter endpoints, we can use the midpoint formula to find the coordinates of the center of the circle. Once we have the center, we can use the distance formula to find the radius. The equation of the circle can then be written as:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) are the coordinates of the center and r is the radius.