Q. The Polar equation of the circle with centre $\left( 2,\frac{\pi}{2} \right)$ and radius 3 units is
A) $r^{2} + 4r\cos\theta = 5$
B) $r^{2} + 4r\sin\theta = 5$
C) $r^{2} - 4r\sin\theta = 5$
D) $r^{2} - 4r\cos\theta = 5$
Explanation
(c)
In centre of circle is $(c,\ \alpha)$ and radius is $a$, then equation of circle is
$r^{2} - 2cr\cos(\theta - \alpha) = a^{2} - c^{2}$
Here, centre $\left( 2,\frac{\pi}{2} \right)$ and radius 3
$\therefore$ Equation of circle is $r^{2} - 2 \times 2r\cos\left( \theta - \frac{\pi}{2} \right) = 3^{2} - 2^{2}$
$\Rightarrow \ r^{2} - 4r\sin{\theta = 5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.