substituting (3 , 4) and (- 1 , 0) in the equation of circle as they lie on it, we get 9 + 16 + 6g + 8f + c = 0 ... (1) 1 + 0 - 2g + c = 0 ... (2) Subtracting (2) from (1), we get ⇒ 24 + 8g + 8f = 0 ⇒ g + f + 3 = 0 ⇒ g + f = - 3 ... (3) Substituting (5 , 3) and (2, 6) in the equation of circle as they also lie on it, we get 4 + 36 + 4g + 12f + c = 0 ... (4) 25 + 9 + 10g + 6f + c = 0 ... (5) From (3) , (4) and (5), we get g = - 1 , f = - 2 c = - 3 g + f + c = - 1 - 2 - 3 = - 6 Hence, option A.