Explanation

(b)
Since, the tangent to the parabola at point $t_{1}$ and $t_{2}$ are $t_{1}y = x + {at}_{1}^{2}$ and $t_{2}y = {at}_{2}^{2}$
Also, tangents are perpendicular to the parabola therefore, $\frac{1}{t_{1}} \bullet \frac{1}{t_{2}} = - 1$ or $t_{2}t_{2} = - 1$
We also know that their point of intersection is
$\left\lbrack {at}_{1}t_{2},\ a\left( t_{1} + t_{2} \right) \right\rbrack$ or $\left\lbrack - a,\ a\left( t_{1} + t_{2} \right) \right\rbrack$
$\therefore$ Point of intersection lie on directrix $x = - a$ or $x + a = 0$