Question

Fin the equation of the straight line passing through the point of intersection of the lines $x+y+1=0$ and $2x-y+5=0$ and containing the point $(5,-2)$.

Answer 1

Line passing through $L_1$ and $L_2$ is given by $L_1+\lambda L_2$

$\Rightarrow L:(x+y+1)+\lambda (2x-y+5)=0$

$\Rightarrow (1+2\lambda )x+(1-\lambda )y+(1+5\lambda )=0$

It passes $(5,-2)$

$\Rightarrow 5+10\lambda -2+2\lambda +1+15\lambda =0$

$\Rightarrow 17\lambda +4=0$

$\Rightarrow \lambda =\frac{-4}{17}$

$\Rightarrow L:\frac{9x}{17}+\frac{21}{17}y-\frac{3}{17}=0$

$\Rightarrow 3x+7y-1=0$.