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  4. 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

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Q. 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

NTA AbhyasNTA Abhyas 2020Straight Lines

Solution:

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