Q. If the lines $3x + 4y + 1 = 0,\ 5x + \lambda y + 3 = 0$ and $2x + y - 1 = 0$ are concurrent, then λ is equal to

A) $- 8$
B) 8
C) 4
D) $- 4$
Explanation

(b)
Given equation of line are
$3x + 4y + 1 = 0$ ….(i)
$5x + \lambda y + 3 = 0$ …(ii)
and $2x + y - 1 = 0$ …(iii)
The intersection point of lines (i) and (iii) is $(1,\ - 1)$.
Since, the line are concurrent, therefore the intersection point $(1,\ - 1)$ lies on line (ii)
$\therefore 5(1) + \lambda( - 1) + 3 = 0\ \ \Rightarrow \ \lambda = 8$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.