Find the equation of the circle passing through the points (1,1), (2,-1)& ( 3,2)

Let the equation of the general form of the required circle be x^2 + y^2 + 2gx + 2fy + c = 0 ……………. (i)According to the problem, the above equation of the circle passes through the points (1, 1), (2, -1) and (3, 2). Therefore,1 + 1 + 2g + 2f + c = 0 2 + 2g + 2f +c = 0……………. (ii)4 +1 + 4g - 2f+ c = 0 5 + 4g - 2f + c = 0……………. (iii)9 + 4 + 6g + 4f + c = 0 13 + 6g + 4f + c = 0……………. (iv)On solving (ii) and (iii), and (iii) and (iv)We obtain c = 4, g = -5/2 and f = -1/2Substituting the values of g, f and c in (i), we obtain the equation of the required circle as x^2 + y^2 - 5x - y + 4 = 0