Question

Find the equation to the straight line:
cutting off an intercept $2$ from the negative direction of the axis of $y$ and inclined at ${30}^o$ to $OX$.

Answer 1

Here $\tan \theta =\frac{2}{x}$

then, $x=\frac{2}{\tan {30}^o}$

$\Rightarrow x=2\sqrt{3}$

$\frac{x}{2\sqrt{3}}+\frac{y}{-2}=1$

$\Rightarrow x-\sqrt{3}y=2\sqrt{3}$

Therfore required equation is

$\Rightarrow x-\sqrt{3}y-2\sqrt{3}=0$