Explanation

(a)
Given , $y^{2} = 16x$, then $a = 4$
Let line perpendicular to given line $y - 3x - 1 = 0\$ is
$x + 3y = \lambda$
$\Rightarrow \ y = - \frac{1}{3}x + \frac{\lambda}{3}$
Here, $c = \frac{\lambda}{3},\ m = - \frac{1}{3}$
$\therefore$ Condition of tangency is, $c = \frac{a}{m}$
$\Rightarrow \ \frac{\lambda}{3} = \frac{4}{- 1/3}\ \ \Rightarrow \ \lambda = - 36$
$\therefore$ Required tangent is$\ x + 3y + 36 = 0$