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

Question

Philoid · Accepted Answer

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.