# 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

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 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