Explanation

(a)
Given, $x = a\left( 1 + \cos\theta \right),\ \ \ y = a\sin\theta$
$\Rightarrow \ \ \ \frac{dx}{d\theta} = a\left( - \sin\theta \right),\ \ \frac{dy}{d\theta} = a\cos\theta$
$\therefore\ \ \ \ \frac{dy}{dx} = \frac{- \cos\theta}{\sin\theta}$
Equating of normal at the given point is
$y - a\sin{\theta = \frac{\sin\theta}{\cos\theta}}\lbrack x - a\rbrack(1 + \cos\theta)\rbrack$
It is clear that in the given options normal passes through the point $(a,\ 0)$