UPSEE Solved Model Paper 4

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.