Question

If the lines $x+3y-9=0,4x+by-2=0$ and $2x-y-4=0$ are concurrent, then $b$ equal to

• A. $-6$
• B. $5$
• C. $1$
• D. $-5$

Answer 1

The correct option is D $-5$

Given lines are concurrent, then there coefficient determinant is zero.

i.e. $\left|\begin{array}{ccc}1& 3& -9\\ 4& b& -2\\ 2& -1& -4\end{array}\right|=0$

$\Rightarrow 1(-4b-2)-3(-16+4)-9(-4-2b)=0$

$\Rightarrow -4b-2+36+36+18b=0$

$\Rightarrow 14b+70=0$

$\Rightarrow b=-5$