Question

The angle between the circles $r=a\cos (\theta -\alpha )$ and $r=b\sin (\theta -\alpha )$ is

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

Answer 1

Answer: (D)

$\frac{\pi }{2}$

Given equation of circles:
$S_1:r=a\cos (\theta -\alpha )$
$S_2:r=b\sin (\theta -\alpha )$
Equation of circle which is perpendicular to $S_2$ is
$r=b\sin (\frac{\pi }{2}+\theta -\alpha )$
$\Rightarrow r=b\cos (\theta -\alpha )$
which is of the form of equation $S_1$
Hence, the angle between the given circles is $\frac{\pi }{2}$