(Solved): PLEASE EXPLAIN EACH STEP AND WRITE CLEARLY SO I CAN FOLLOW, thank you :) Consider the parabola wi ...

PLEASE EXPLAIN EACH STEP AND WRITE CLEARLY SO I CAN FOLLOW, thank you :)

Consider the parabola with equation $4cy=x^2$. Its focus is at the point $(0,c)$, its directrix is the line $y=?c$, and the parabola consists of all points whose distance from the focus is equal to the distance from the directrix. If you make the parabola out of reflective material, i.e., it is a parabolic mirror, then you shine a ray of light vertically downwards onto the parabola, the parabolic mirror reflects all of the light to the focus. Prove this property!