Question

Find the equation of a line making an angle of ${150}^o$ with the $x-axis$ and cutting off intercept $2$ from $y-axis$

• A. $2\sqrt{3}x+\sqrt{3}y=2\sqrt{3}$
• B. $\sqrt{3}x+y=2\sqrt{3}$
• C. $\sqrt{3}x-y=2\sqrt{3}$
• D. $x+\sqrt{3}y=2\sqrt{3}$

Answer 1

The correct option is D $x+\sqrt{3}y=2\sqrt{3}$

Equation of any line is given by $y=mx+c$

where $m=\tan \theta$, $\theta$ is angle made by $x-$ axis

$m=\tan {150}^o=\tan ({180}^o-{30}^o)$

$=-\tan {30}^o$

$=-\frac{1}{\sqrt{3}}$

also when $x=0$, we have $y=2$.

so $y=\frac{-x}{\sqrt{3}}+c$ put $x=0$ and $y=2$

$2=c$

so equation is $y=\frac{-x}{\sqrt{3}}+2\Rightarrow x+y\sqrt{3}=2\sqrt{3}$.