Question

Show that the equation of the line passing through the origin and making an angle $\theta$ with the line $y=mx+c$ is $\frac{y}{x}=\frac{m\pm \tan \theta }{1\mp m\tan \theta }$.

Answer 1

Slope of the line be h

$\tan \theta =\pm \frac{m-h}{1+mh}$

$\pm (1+mh)\tan \theta =(m-h)$

$\pm \tan \theta +m=h(1\mp m\tan \theta )$

$h=\frac{m\pm \tan \theta }{1\mp m\tan \theta }$