The conic sections have become a smaller and smaller part of high school math in the U.S. Nevertheless, they are interesting, and the advent of geometric construction software has made them more accessible. I share a fair amount of possibly useful materials about them on this site.
One conic section that's not going anywhere is the parabola. On my Parabolas and Quadratics page, I have links to much curriculum, ranging from Algebra 1 to "Teachers' Mathematics." The emphasis there is mostly on algebra. On this page, I mostly link to the geometry of the conic sections.
- Geometry of the Parabola
- In two dimensions (definition, construction, reflection property, all parabolas are similar)
- In three dimensions (the parabola really is a conic section!)
- Parabola Similarity (worksheet, using GeoGebra)
- Geometry of the Ellipse
- In two dimensions (two definitions, constructions, reflection property)
- In three dimensions (slicing a cone or a cylinder)
- Algebra connection (worksheet)
Paper-folding Conics (hands-on lab by Rachel Chou)
A related problem (surprisingly): Soccer Angles