well, you know that a parabola's equation with vertex at (0,0) is
x^2 = 4py
The length of the latus rectum is 4p, and the distance from the focus to the vertex is p. So,
tan θ/2 = 2p/p = 2
for all parabolas, show that the angle between the line segment joining endpoints of the latus rectum to the vertex is 2 arctan 2
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