Final answer:
To find the equation of a circle, determine the center and radius. The center is the midpoint of the diameter endpoints and the radius is half the length of the diameter. The equation of the circle is (x - 1)^2 + (y + 1)^2 = 13.
Step-by-step explanation:
To find the equation of a circle, we need to determine the coordinates of the center and the radius. The center can be found by taking the midpoint of the two given endpoints of the diameter.
The radius is half the length of the diameter.
First, find the midpoint of the two given endpoints (-1,-4) and (3,2).
The midpoint is calculated by finding the average of the x-coordinates and the average of the y-coordinates. The midpoint is ((-1 + 3)/2, (-4 + 2)/2) = (1, -1).
Next, calculate the radius by finding the distance between one of the endpoints and the center. The distance formula is given by sqrt((x2 - x1)^2 + (y2 - y1)^2).
Considering (-1,-4) as the endpoint, the radius is sqrt((1 - (-1))^2 + (-1 - (-4))^2) = sqrt(4 + 9) = sqrt(13).
Therefore, the equation of the circle is (x - 1)^2 + (y + 1)^2 = 13.