Parabolic reflectors for giant halogen lamps

The car dealership had large halogen lamps - bigger versions of those that I used to put inside an overhead projector (OHP). And they were surrounded by parabolic silver reflectors. A parabola is the curve that you get if you plot y against x-squared. It is an important shape for a reflector because it has a clear focal point. In other words, any parallel beams of light coming in reflect back out through a single point. That is not true for a spherical reflector. Rays that are parallel are said to have come from infinity. So these lamp shades work in reverse. If you put the bulb in at the focal point, the rays that go upwards back into the lamp shade are reflected back out parallel in a beam.