Question

The polar equation of the line passing through $(4,\frac{2\pi }{3})$ and perpendicular to the line joining the origin to this point is

• A. $r\cos (\theta -\frac{\pi }{3})=4$
• B. $r\cos (\theta -\frac{2\pi }{3})=4$
• C. $r\cos (\theta -\pi )=4$
• D. $r\cos (\theta -\frac{4\pi }{3})=4$

Answer 1

Answer: (B)

$r\cos (\theta -\frac{2\pi }{3})=4$

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, $\alpha =\frac{2\pi }{3}$, $p=4$
So, the required equation is $r\cos (\theta -\frac{2\pi }{3})=4.$