Answer:
Explanation:
The center of a circle is the midpoint of its diameter. The midpoint of the segment whose endpoints are (-2,5) and (4,7) is:
((-2 + 4)/2, (5 + 7)/2) = (1, 6)
Therefore, the center of the circle is (1, 6), and its radius is half the length of the diameter:
r = sqrt((4 - (-2))^2 + (7 - 5)^2)/2 = sqrt(40)/2 = sqrt(10)
The equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values of (h, k, r) into the equation, we get:
(x - 1)^2 + (y - 6)^2 = 10
Therefore, the equation of the circle with the segment whose endpoints are (-2,5) and (4,7) as the diameter is:
(x - 1)^2 + (y - 6)^2 = 10