if the lines ax+2y+1=0, bx+3y+1=0, cx+4y+1=0 are concurrent then a,b,c are in:

a) AP

b)GP

c)HP

d)Neither GP or AP

Open in App

Solution

Answer: (a) a, b, c are in A.P.

ax + 2y + 1 = 0

bx + 3y + 1 = 0

cx + 4y + 1 = 0 are concurrent lines

a

2

1

∴

b

3

1

= 0

c

4

1

∴ a(3 – 4) – (b – c)(2) + 1(4b – 3c) = 0

∴ – a – 2b + 2c + 4b – 3c = 0

∴ – a + 2b – c = 0

∴ 2b = a + c

∴ a, b, c are in A.P.

Suggest Corrections

Similar questions

a x + 2 y + 1 = 0

b x + 3 y + 1 = 0

c x + 4 y + 1 - 0

a, b, c

a x + 2 y + 1 = 0, b x + 3 y + 1 = 0

c x + 4 y + 1 = 0

a, b, c

A . P .

If a, b, c are in A.P., prove that the straight lines $a x + 2 y + 1 = 0, b x + 3 y + 1 = 0$ and $c x + 4 y + 1 = 0$ are concurrent.

a, b, c

a x + 2 y + 1 = 0

b x + 3 y + 1 = 0

c x + 4 y + 1 = 0

Join BYJU'S Learning Program