The combined equation of a pair of lines passing through the origin and inclined at $60^{\circ}$ and…
The combined equation of a pair of lines passing through the origin and inclined at $60^{\circ}$ and $30^{\circ}$ respectively with $\mathrm{x}$-axis is
$\sqrt{3}\left(x^2+y^2\right)=2 x y$
$\sqrt{3}\left(x^2+y^2\right)=4 x y$
$4\left(x^2+y^2\right)=\sqrt{3} x y$
$2\left(x^2+y^2\right)=\sqrt{3} x y$
Solution
The equation of two required lines are $y=\sqrt{3} x$ and $y=\frac{1}{\sqrt{3}} x$ Their combined equation is
$(\sqrt{3} x-y)(x-\sqrt{3} y)=0 \text { i.e. } \sqrt{3} x^2-4 x y+\sqrt{3} y^2=0$