The joint equation of the lines through the origin trisecting angles in first and third equadrant is
The joint equation of the lines through the origin trisecting angles in first and third equadrant is
$\sqrt{3}\left(x^{2}-y^{2}\right)+4 x y=0$
$\sqrt{3}\left(x^{2}+y^{2}\right)-4 x y=0$
$\sqrt{3}\left(x^{2}+y^{2}\right)+4 x y=0$
$\sqrt{3}\left(x^{2}-y^{2}\right)-4 x y=0$
Solution
Equation line $\mathrm{L}_{1}$ is $\mathrm{y}=\tan 30^{\circ} \mathrm{x}$
$y=\frac{1}{\sqrt{3}} x \Rightarrow x-\sqrt{3} y=0 ...(1)$
Equation of line $\mathrm{L}_{2}$ is $\mathrm{y}=\tan 60^{\circ} \mathrm{x}$
$y=\sqrt{3} x \Rightarrow \sqrt{3} x-y=0 ...(2)$
$\therefore$ Joint equation is
$(x-\sqrt{3} y)(\sqrt{3} x-y)=0 \Rightarrow \sqrt{3}\left(x^{2}+y^{2}\right)-4 x y=0$
