Straight Line Question 48

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

Options:

A)A. P.

B)G. P.

C)H. P.

D)None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • It is given that the lines $ ax+2y+1=0 $ , $ bx+3y+1=0 $ and $ cx+4y+1=0 $ are concurrent, therefore $ | \begin{matrix} a & 2 & 1 \\ b & 3 & 1 \\ c & 4 & 1 \\ \end{matrix} |=0 $
    Þ $ -a+2b-c=0\Rightarrow 2b=a+c $
    Þ $ a,b,c $ are in A. P.