3. Find the centre of a circle passing through points (6, -6), (3, -7) and (3, 3).

Let A = (6, -6), B = (3, -7), C = (3, 3) are the points on a circle. If O is the centre, then OA = OB = OC (radii are equal) If O = (x, y) then OA = √[(x – 6)2 + (y + 6)2] OB = √[(x – 3)2 + (y + 7)2] OC = √[(x – 3)2 + (y – 3)2] Choose: OA = OB, we have After simplifying above, we get -6x = 2y – 14 ….(1) Similarly: OB = OC (x – 3)2 + (y + 7)2 = (x – 3)2 + (y – 3)2 (y + 7)2 = (y – 3)2 y2 + 14y + 49 = y2 – 6y + 9 20y =-40 or y = -2 Substituting the value of y in equation (1), we get; -6x = 2y – 14 -6x = -4 – 14 = -18 x = 3 Hence, the centre of the circle located at point (3,-2).