Question

Find the combined equation of lines passing through the origin and having inclination $\frac{\pi }{3}$ and $\frac{5\pi }{3}$

Answer 1

Lines are $y=\left(\tan \frac{\pi }{3}\right)x\Rightarrow \sqrt{3}x-y=0$

and $y=\left(\tan \frac{5\pi }{3}\right)x\Rightarrow \sqrt{3}x+y=0$

$\therefore$ the combined equation is

$(\sqrt{3}x-y)(\sqrt{3}x+y)=0$

$\Rightarrow 3x^2-y^2=0$