The joint equation of pair of lines through the origin and making an equilateral triangle with the line…

The joint equation of pair of lines through the origin and making an equilateral triangle with the line $y=5$ is
  1. $3 x^2-y^2=0$
  2. $5 x^2-y^2=0$
  3. $x^2-3 y^2=0$
  4. $\sqrt{3} x^2-y^2=0$

Solution

$\begin{aligned} & y=\tan 60^{\circ} x \Rightarrow y=x \\ & y=\tan 120^{\circ} x \Rightarrow y=-x \\ & \text { joint equation }=(x-y)(x+y)=0 \\ & \Rightarrow 3 x^2-y^2=0\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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