Question

Find the joint (combined) equation of the pair of lines through the points $(1,0)$ and $(2,0)$
and each making an angle of ${30}^0$ with the X-axis.

Answer 1

Let ,

Required equation makes an angle with positive x-axis =$\theta$

$\theta ={30}^0$

Now slop of equation is $m=\tan \theta =\tan {30}^o=\frac{1}{\sqrt{3}}$

Point through which pass line is =(1,0)

Now ,

$y-0=\frac{1}{\sqrt{3}}(x-1)$

$\sqrt{3}y=x$

$x-\sqrt{3}y=0$

Required equation is

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

$x^2+3y^2=0$

This is the answer