Question

Line $L=0$ implied by $x+4y+7=0$ is concurrent with the lines $x-2y+1=0$ and $3x-4y+\lambda =0$, then the value of $\lambda$ is

• A. $2$
• B. $1$
• C. $-4$
• D. $5$

Answer 1

The correct option is D $5$

Here $L=0$ implies $x+4y+7=0$
Since is concurrent with $x-2y+1=0$, therefore they have an unique solution.
Therefore upon subtracting we get
$6y+6=0$
$y=-1$ and hence $x=-3$
Therefore the point of intersection of these two lines is $(-3,-1)$
This will also be a solution of $3x-4y+\lambda =0$
Therefore substituting $x=-3$ and $y=-1$ we get
$-9+4+\lambda =0$
$\lambda =5$