Answer:To find the equation of a circle, we need the center coordinates and the radius of the circle. In this case, we are given the center at (4, -9) and an endpoint at (3, 2).
To find the radius, we can use the distance formula between the center and the endpoint. The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the given values, we have:
d = sqrt((3 - 4)^2 + (2 - (-9))^2)
= sqrt((-1)^2 + (11)^2)
= sqrt(1 + 121)
= sqrt(122)
So, the radius of the circle is sqrt(122).
Now, we can write the equation of the circle using the standard form:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) represents the coordinates of the center, and r represents the radius.
Substituting the values, we have:
(x - 4)^2 + (y - (-9))^2 = (sqrt(122))^2
(x - 4)^2 + (y + 9)^2 = 122
Therefore, the equation of the circle with a center at (4, -9) and an endpoint at (3, 2) is (x - 4)^2 + (y + 9)^2 = 122.
Explanation: