Question

A straight line makes an angle $\alpha$ with the positive direction of $x$-axis, where $\cos \alpha=\frac{\sqrt{3}}{2}$. If it passes through $(0,-2)$, then its equation is

• A. $\sqrt{3} x+y+2=0$
• B. $\sqrt{3} y+x+2=0$
• C. $\sqrt{3} y+x+2 \sqrt{3}=0$
• D. $\sqrt{3} y-x+2 \sqrt{3}=0$
• E. $\sqrt{3} x+y-2 \sqrt{3}=0$

Answer 1

Answer: (D)

Given, $\cos \alpha=\frac{\sqrt{3}}{2}$
$ \Rightarrow \sin \alpha=\sqrt{1-\cos ^2 \alpha} $
$ \sin \alpha=\sqrt{1-3 / 4}=\frac{1}{2}$
$ m=\tan \theta=\frac{1}{\sqrt{3}}$
Required equation of line is $y+2=\frac{1}{\sqrt{3}}(x-0)$
$\Rightarrow \quad \sqrt{3} y-x+2 \sqrt{3}=0$