Passing through the origin and having slopes 2 and 3. - Vidyadip

Question

Passing through the origin and having slopes $2$ and $3$.

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Answer

We know that the equation of the line passing through the origin and having slope $m$ is $y=m x$.
Equations of the lines passing through the origin and having slopes 2 and 3 are $y=2 x$ and $y=3 x$ respectively.
i.e. their equations are
$2 x-y=0$ and $3 x-y=0$ respectively.
$\therefore$ their joint equation is $(2 x-y)(3 x-y)=0$
$\therefore 6 x^2-2 x y-3 x y+y^2=0$
$\therefore 6 x^2-5 x y+y^2=0$.

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