Answer:(x - 1)² + (y + 1/2)² = 65/4Step-by-step explanation:Given: the endpoints of the diameter are (3, 3) and (-1, -4). a( To determine the center of this circle, find the midpoint of the line segment connecting these two points: 3 - 1x = ----------- 2and -1y = ---------- 2The center is at x = 1 and y = -1/2: (1, -1/2).b) The radius is half the diameter. The diameter is the distance between the two endpoints given, that is, the distance between (-1, -4) and (3, 3):diameter = √(4² + 7²) = √(16 + 49) = √65; therefore,radius = (1/2)√65.square of the radius = r² = 65/4The general equation of a circle with center at (h, k) and radius r is(x - h)² + (y - k)² = r². In this case, the equation is:(x - 1)² + (y + 1/2)² = 65/4