Topic: Conic Sections

Subtopic: General and Degenerate Conics

**Overview**

In calculus you will be expected to know how to identify and graph conics from both the __general form of a conic__, ax^{2}+bx+cy^{2}+dy+e=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 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!

**Objectives**

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

- 7.5.1 Understand the general equation of a conic section
- 7.5.2 Algebraically convert from the general form and standard form of a conic and visa versa using CTS as needed
- 7.5.3 Identify a conic from the general form equation
- 7.5.4 Understand degenerate conics including their equations, graphs, formation (in terms of slicing the double cone), and how to identify them from the general equation of a conic

**Terminology**

Define: general form of the equation of a conic section, degenerate conic

**Supplemental Resources**

Download/Print: Conic Sections Formula Sheet (by Prof. Louise Hoover, ret. Clark College)