If the double ordinate of the parabola $y^2=8x$  is of length 16 then the angle subtended by it at the vertex of the parabola is

The given parabola is $y^2=8x$

The end points of the double ordinate of the parabola are  $\left(2t^2,\pm 4t\right)$

 length of Double  ordinate $=16\Rightarrow 8t=16\Rightarrow t=2$

The end points of the double ordinate are $A(8,-8),B(8,8)$.

Vertex of the parabola $O(0,0)$

$\therefore OA=8\sqrt{2},OB=8\sqrt{2}\text{ and }AB=16\Rightarrow O{A}^2+O{B}^2=A{B}^2\text{. Hence }\mathrm{\angle }AOB=\pi /2$

The angle subtended by double ordinate at its vertex $=\pi /2$