Range of angle made by focal chord of a parabola at the vertex.

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How to determine the range of angle which a focal chord of a parabola (considering a standard parabola $ y^2 =4ax $) subtend at the vertex.

My attempt:Take $ t_1$ and $ t_2$ two points on the para bola. We have the relation $ t_1 t_2 =-1$. How to move further?