The triangle formed by the tangents to the parabola  $y^2=4ax$ at  the ends of the latusrectum and the double 

ordinate through the focus, is 

Since the tangents at the end-points of a focal 

chord intersect at right-angles on the directrix. 

So, the triangle is right angled. The equations 

of the tangents at  $L(a,2a)$ and $L^{\mathrm{\prime }}(a,-2a)$  are 

$x-y+a=0$ and $x+y+a=0$ respectively. These two intersect

at $P(-a,0)$ 

We have,                        PL= 2$\sqrt{2}$a= PL'

Hence, the triangle is right-angled isosceles