Course: College Algebra
Topic: Conic Sections
Subtopic: General and Degenerate Conics


In calculus you will be expected to know how to identify and graph conics from both the general form of a conic, `ax^2+bxy+cy^2+dx+ey+f=0`, and the standard form. The key to understanding the relationship between these two forms of a conic's equation and the graph is the process of converting from one to the other including via completing the square.

Sometimes, depending on the a b c d e f constants, the equation will result in a point, line, or two intersecting lines. These cases are called the degenerate conics and occur when the plane slicing the double cone does so at particularly interesting places or at specific angles. These degenerates provide a great connection between the algebra of conics and the visual experience. Cool stuff!


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: general form of the equation of a conic section, degenerate conic

Supplemental Resources

Download/Print one of the following formula Sheets, whichever works best for you. You may annotate your formula sheet and refer to it during a test.

Summary of Conic Sections provides a thorough list of all the conic sections and their equations.

rev. 2020-11-29