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 $y+2=\frac{1}{\sqrt{3}}(x-0)$
$\Rightarrow \sqrt{3}y-x+2\sqrt{3}=0$