The center of a circle is the midpoint of its diameter. To find the midpoint of AB, we add the x-coordinates of A and B and divide by 2, and add the y-coordinates of A and B and divide by 2:
Midpoint = ((-4 + 3)/2, (2 + 2)/2) = (-0.5, 2)
So the center of the circle is at (-0.5, 2).
The radius of the circle is half the length of the diameter. To find the length of AB, we use the distance formula:
AB = sqrt((3 - (-4))^2 + (2 - 2)^2) = sqrt(49) = 7
So the radius of the circle is 7/2.
The equation for a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Plugging in the values we found, we get:
(x - (-0.5))^2 + (y - 2)^2 = (7/2)^2
Simplifying, we get:
(x + 0.5)^2 + (y - 2)^2 = 49/4
Therefore, the equation for the circle is (x + 0.5)^2 + (y - 2)^2 = 49/4.