Question

The angle made by the perpendicular of the line $r(\cos \theta +\sqrt{3}\sin \theta )=5$ with the polar axis is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{6}$

Answer 1

Answer: (B)

$\frac{\pi }{3}$

The equation of line at a distance $p$ from the normal and the normal make an angle $\alpha$ with polar axis is
$r\cos (\theta -\alpha )=p$
Given equation is $r(cos\theta +\sqrt{3}sin\theta )=5$
$\Rightarrow r(\frac{1}{2}cos\theta +\frac{\sqrt{3}}{2}\sin \theta )=\frac{5}{2}$
$\Rightarrow r\cos (\theta -\frac{\pi }{3})=\frac{5}{2}$
So, here $\alpha =\frac{\pi }{3}.$