# Homework Help: Prove that rays that reflect from a Parabolic Dish cut the Z axis in the same point?

1. Dec 15, 2011

### gipc

I have the following "Parabolic Dish" z=c(x^2+y^2)
I have to prove that all the reflecting light rays that hit that dish go through the same point Q in the Z axis, and then I have to find said point Q.

I've thought of reducing the problem to 2 dimensions. Started with the parabola y = ax^2. Tried to find the angle that some line x = c strikes the curve but couldn't find the correct angle. Maybe do some gradient magic?

I'm unsure really, how to set it all together for a good proof, and how to finally find the point Q.

2. Dec 15, 2011

### SammyS

Staff Emeritus
Re: Prove that rays that reflect from a Parabolic Dish cut the Z axis in the same poi

I doubt that this is the complete problem as given. The incident rays would all need to be parallel to the z-axis.

3. Dec 15, 2011

### gipc

Re: Prove that rays that reflect from a Parabolic Dish cut the Z axis in the same poi

Ohh, yes, obviously they are indeed parallel :)