Parabolas are a central topic in high school algebra classes, but, perhaps because of the rigid separation between algebra and geometry classes in the US secondary curriculum, we do not usually treat them as geometric objects. While most teachers are aware of some of the parabola's geometric properties, few of us are familiar with the proofs of those properties.
- On my Web site, I present the basic geometry of the parabola: the geometric definition in terms of focus and directrix, the construction, the reflection property, and "all parabolas are similar". I have updated that page with the addition of a few new GeoGebra applets. Check it out!
Thanks to Bruce Cohen for his GeoGebra help!