Explanation

(a)
Given, $r = \sqrt{3}\sin\theta + \cos\theta$
Put $x = r\cos\theta,\ y = r\sin\theta$
$\therefore\ \ \ r = \sqrt{3}\frac{y}{r} + \frac{x}{r}$
$\Rightarrow \ \ \ r^{2} = \sqrt{3}y + x$
$\Rightarrow x^{2} + y^{2} - \sqrt{3}y - x = 0$
$\therefore$Radius$= \sqrt{\left( \frac{\sqrt{3}}{2} \right)^{2} + \left( \frac{1}{2} \right)^{2}} = 1$