Question

The polar equation of the circle with center $(2,\frac{\pi }{2})$ 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. $r^2-4r\cos \theta =5$

Answer 1

The correct option is C $r^2-4r\sin \theta =5$

General equation of circle in polar form is $r^2-2r{r}_0\cos (\theta -\gamma )+{r_0}^2=a^2$
where, $(r_0,\gamma )$ is center and $a$ is radius
$\Rightarrow r^2-2r\left(2\right)\cos (\theta -\frac{\pi }{2})+2^2=3^2$
$\Rightarrow r^2-4r\sin \theta =5$