Question

Find the joint equation of pair of lines passing through the origin having slopes 2 and -2

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Slopes of the given lines are 2 and -2}$

$\underline{\textbf{To find:}}$

$\textsf{Joint equation of pair of lines passing through origin}$

$\textsf{having slopes 2 and -2}$

$\underline{\textbf{Solution:}}$

$\textbf{Formula used:}$

$\textsf{The equation of straight line passing through origin}$

$\textsf{and having slope m is}\;\;\boxed{\textbf{y=mx}}$

$\mathsf{Here,}$

$\mathsf{Slopes:\;m_1=2\;\&\;m_2=-2}$

$\textsf{Equation of the lines are}$

$\mathsf{y=m_1\,x\;\;\&\;\;y=m_2\,x}$

$\mathsf{y=2\,x\;\;\&\;\;y=-2\,x}$

$\mathsf{2\,x-y=0\;\;\&\;\;2\,x+y=0}$

$\therefore\textsf{Their joint equation is}$

$\mathsf{(2x-y)(2x+y)=0}$

$\mathsf{(2x)^2-y^2=0}$

$\implies\boxed{\mathsf{4x^2-y^2=0}}$

$\underline{\textbf{Find more:}}$

The angle between the lines ,2x+3y=5 and 3x-2y=7  

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