Question

If the lines ax + 12y + 1 = 0, bx + 13y + 1 = 0 and cx + 14y – 1 = 0 are concurrent, then a, b, c are in 

A. H.P. 

B. G.P. 

C. A.P. 

D. none of these

Answer 1

The given lines are 

ax + 12y + 1 = 0 … (1)

bx + 13y + 1 = 0 … (2) 

cx + 14y + 1 = 0 … (3) 

It is given that (1), (2) and (3) are concurrent.

⇒ a(13 – 14) – 12(b – c) + 14b – 13c = 0 

⇒ -a – 12b + 12c + 14b – 13c = 0 

⇒ -a + 2b – c = 0 

⇒ 2b = a + c 

Hence, a, b and c are in AP.