Question

The radius of the circle $r^2-8r\cos (\theta -\frac{\pi }{3})=9$ is

• A. $3$
• B. $4$
• C. $5$
• D. $8$

Answer 1

The correct option is C $5$

Given, $r^2-8r\cos (\theta -\frac{\pi }{3})=9$
$\Rightarrow r^2-2r\left(4\right)\cos (\theta -\frac{\pi }{3})+4^2=5^2$
On comparing with $r^2-2r{r}_0\cos (\theta -\gamma )+{r_0}^2=a^2$
where, $(r_0,\gamma )$ is center and $a$ is radius
Radius of circle is $a=5$
Ans: C