Question

for all parabolas, show that the angle between the line segment joining endpoints of the latus rectum to the vertex is 2 arctan 2

Answer 1

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