Traditional Culture Encyclopedia - Photography and portraiture - A straight line passing through the focus f of the parabola intersects with the parabola at points A and B. If both points A and B are on straight lines A2 and B2, then ∠A2FB2=?

A straight line passing through the focus f of the parabola intersects with the parabola at points A and B. If both points A and B are on straight lines A2 and B2, then ∠A2FB2=?

Solution:

Let the intersection of the collimation line and the x axis be k,

∫ the projections of a and b on the parabolic quasiline are A 2 and B 2,

From the definition of parabola, AA 2 =AF,

∴∠AA 2 F=∠AFA 2，

And ∠AA 2 F=∠A 2 FK is obtained by equal internal dislocation angles,

∴∠AFA 2 =∠A 2 FK。

It can also be proved that ∠ bfb2 = ∠ b2fk.

By ∠ AFA2+∠ A2FK+∠ BFB2+∠ B2FK =180

∴∠A 2 FK+∠B 2 FK=∠A 2 FB 2 =90