Pair of Straight Lines — Maths STD 12 Science — Question

$\therefore$ their slopes are $m_1=\tan 60^{\circ}=\sqrt{3}$ and

$m_2=\tan 120^{\circ}=\tan \left(180^{\circ}-60^{\circ}\right)$

$=-\tan 60^{\circ}=-\sqrt{3}$

Since the lines pass through the origin, their equa-tions are

$y=\sqrt{3} x$ and $y=-\sqrt{3} x$

i.e., $\sqrt{3} x-y=0$ and $\sqrt{3} x+y=0$

∴ the joint equation of these lines is

$\begin{aligned} & (\sqrt{3} x-y)(\sqrt{3} x+y)=0 \\ & \therefore 3 x^2-y^2=0\end{aligned}$