Explanation

(a)
The coordinates of end point of latusrectum are $(a,\ 2a)$ and $(a,\ - 2a)\ ie$, $(3,\ 6)$ and $(3,\ - 6)$
The equation of directrix is $x = - 3$
The equation of tangents from the above points are $6y = 6(x + 3)$ and $- 6y = 6(x + 3)$
$\Rightarrow x - y + 3 = 0$ and $x + y + 3 = 0$
The intersection point is $( - 3,\ 0)$
The equation of directrix of the parabola $y^{2} = 12x$ is $x = - 3$
$\Rightarrow$ Intersection point $( - 3,\ 0)$ lies on the directrix