The tangents at the ends of a focal chord of a parabola  $y^2=4ax$ intersect on the directrix at an angle of

Let $A\left(a{t}_1,2a{t}_1\right),B\left(a{t}_2^2,2a{t}_2\right)$

 AB is a focal chord $\Rightarrow t_1{t}_2=-1$

Slope of the tangent at A $\times$ slope of the tangent at $B=\frac{1}{t_1}\times \frac{1}{t_2}=\frac{1}{t_1{t}_2}=-1$

The tangents are at right angles'