Skateboard ramps aren’t the only parabolic (curved or bowl-shaped) structures in real life; they pop up in places you never would’ve guessed...

ramp

Parabolas have some very interesting properties. If you put a light at a particular point (called the “focus”) of a parabolic mirror (p-mirror), particles of light start moving away from the light source in all directions, but after bouncing off the mirror, they all move in the same direction and thus are able to shine light on something very far away. Enter car headlights!

The telescope is this functionality in reverse. Particles of light traveling from far away (a star perhaps) bounce off a p-mirror and end up in the same place – the focus. In this way you can collect light from something that appears very dim to the eye. This also works in the case of sending and receiving television and radio signals via satellite dishes!

A microphone placed at the focus of a p-mirror would explain how sportscasters can listen in on what is being said at a great distance on the playing field.

In short: a parabolic mirror serves to transform radial motion (motion to or from a central point) into parallel motion or vice versa...

And you thought maths was boring!

Source: Mathforum