Usefulness of Conic Sections Conic sections are a frequent target for dropping when attempting to make room for other topics in advanced algebra and precalculus courses.  A common argument in favor of dropping them is that typical first-year calculus doesn't use conic sections at all.  Do conic sections come up in typical intro-level undergraduate courses?  In typical prelim grad-level courses?  If so, where?

Conic sections should definitely be retained. If you don't cover conic sections, then what other examples can you cover?
Lines? Too simple. General curves? Insufficiently concrete.
Examples are very important for illustrating the general theory and techniques.
Also, in a multivariable calculus course, typical examples will involve quadric surfaces. Here conic sections will come into play, since hyperplane sections (or "level curves") of quadric surfaces are conic sections.
