On Oct 3, 2012, at 11:17 AM, Peter Duveen <pduveen@yahoo.com> wrote:

I have a student who is prepping for an advanced algebra class, which is one step beyond Algebra II. Conic sections are not covered. The parabola and the Hyperbola are, but more from an algebraic standpoint. Seems to me conic sections would be a good idea, since it unifies the various topics in analytic geometry.

In college I took an introduction to orbital mechanics, the text was this one...

Here is a similar course at MIT Openware...

What we did in algebra 2 with conic sections didn't supply the physics behind the developments in this course but it did supply much of the analytic geometry and terminology. Not surprising, since 2-body orbits are conic sections. Conic sections are also useful in the treatment of elementary (high school) optics.

I think you head it on the head, analytic geometry. Extremely important in engineering and physics, maybe not so much in mathematics.

Bob Hansen