Final answer:
To find the equation of a circle with given endpoints of a diameter, find the midpoint and distance between the endpoints. The center is the midpoint and the radius is half the distance. The equation of the circle is (x-1)^2 + (y-2)^2 = 10.
Step-by-step explanation:
To find the equation of a circle, we need the center and radius of the circle. The center of the circle can be found by taking the midpoint of the diameter, which is the average of the x-coordinates and the average of the y-coordinates. The radius of the circle is half the length of the diameter.
For the given diameter with endpoints (4,3) and (-2,1), the midpoint is ((4+(-2))/2, (3+1)/2) = (1, 2). The distance between the endpoints is the diameter, which can be found using the distance formula as sqrt((-2-4)^2 + (1-3)^2) = sqrt(36+4) = sqrt(40). Therefore, the radius is sqrt(40)/2 = sqrt(10).
Putting it together, the equation of the circle is (x-1)^2 + (y-2)^2 = 10.