Question

The number of values of $p$ for which the lines $x+y-1=0,px+2y+1=0$ and $4x+2py+7=0$ are concurrent is equal to

• A. $0$
• B. $2$
• C. $1$
• D. Infinite

Answer 1

Answer: (C)

$\left|\begin{array}{ccc}1& 1& -1\\ p& 2& 1\\ 4& 2p& 7\end{array}\right|=0$
$\Rightarrow 2p^2+9p-26=0$
$\Rightarrow p=\frac{-13}{2},2$
$p=2$ is rejected because at $p=2$ all $3$ lines becomes parallel
$\Rightarrow$ Hence, $p=\frac{-13}{2}$