# Conic Sections Cheat Sheet

## General Equation Features

The **general equation** of a conic section is

The **discriminant **is the number

## Graph Features

### On the Curve

**Vertex**:** **an extreme point or turning point

*Not* on the Curve

*Not*on the Curve

**Focus:** a point used to define the conic section, the curve bends around this point. (Plural: foci)

**Directrix:** a straight line used to define the conic section. (Plural: directrices)

A **conic section** is the set of all points *P *such that the distance from *P *to the nearest **focus **is a constant multiple of the distance from *P* to the nearest **directrix**.

### Eccentricity

The **eccentricity ***e *of a conic section is the distance from any point *P *on the curve to the nearest focus, divided by the distance from *P* to the nearest directrix.

## A Note About Circles

A **circle **is a special type of ellipse, where *A = B *in the general conic equation. For a circle,

**Eccentricity**is defined as*e*= 0.The center is the focus.

There are no directrices.

There are no vertices.

Since the eccentricity of a circle is 0, the eccentricity of a conic can be thought of as how much the curve deviates from being circular.

Formulas in this tutorial were generated with **QuickLaTeX.com**