Question

If the lines ax+y+1=0, x+by+1=0 and x+y+c=0 (a,b,c being distinct and different from 1) are concurrent, then (1/1 -a) + 1/1 - b  + 1/1 - c =

(a)  0

(b)  1

(c)  1/ a + b + c

 (d)  None

Answer 1

Correct option  (b) 1

Explanation:

c₂ → c₂ –c₁ ,c₃ → c₃ – c₁

a(b - 1)(c - 1) - (1 - a)(c - 1) +(1 - a)(1 - b) = 0

divide by (1 - a)(1 - b)(1 - c) we get

a/1 - a + 1/1 - b + 1/1 - c = 0

1/1 - a + 1/1 - b + 1/1 - c = 1