Question

The angle between the line 2x+y+1=0 and x+ky+5=0 is 90° then k=

Answer 1

$\textsf{Concept:}$

$\textsf{slope of the line ax+by+c=0 is }\mathsf{m=\frac{-coefficient\;of\;x}{coefficient\;of\;y}=\frac{-a}{b}}$

$\textsf{Given lines are }$

$\mathsf{2x+y+1=0\;\;and\;\;x+ky+5=0}$

$\textsf{Slope of 2x+y+1=0 is }\maths{m_1=\frac{-2}{1}=-2}$

$\textsf{Slope of x+ky+5=0 is }\maths{m_2=\frac{-1}{k}}$

$\textsf{since the lines are perpendicular to each other, }\mathsf{m_1{\times}m_2=-1}$

$\mathsf{\implies\;-2{\times}(\frac{-1}{k})=-1}$

$\mathsf{\implies\;\frac{2}{k}=-1}$

$\mathsf{\implies\;2=-k}$

$\mathsf{\implies\boxed{k=-2}}$

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