Satellite Dish Parabola Fastest Proof For Theory That Parallel Rays Entering Parabola Hit Focus?

Fastest proof for theory that parallel rays entering parabola hit focus? - satellite dish parabola

Please, no load, with the exception of derivatives, if possible. We have this property in the class one million times (that is, like satellite dishes) work, but not a teacher gave a test. I found it here a while, but it is too long for my taste (~ 1 page).