# Hyperbolas

## Common Hyperbola Features

There are two standard forms for the equation of a hyperbola, shown below.

Hyperbolas have the following features

**Two foci**and**two directrices****Eccentricity****greater than 1****Center:**the midpoint of the line segment joining the foci**Two vertices:**on the line segment joining the foci**Two asymptotes:**lines passing through the center which bound the curve

We can divide hyperbolas into two types: those that **open ****left and right**, and those that **open ****up and down**.

The information we can find from the equation of each type of hyperbola is summarized in the table below.

## Graphs of Hyperbolas

### Hyperbolas Opening Left and Right

A hyperbola with an equation of this form **opens ****left and right**.

Use the sliders below to change the values of *a*, *b*, *h*, and *k*, and see different hyperbolas opening left and right. The hyperbola is graphed along with its foci, directrices, and asymptotes.

### Hyperbolas Opening Up and Down

A hyperbola with an equation of this form **opens ****up and down**.

Use the sliders below to change the values of *a*, *b*, *h*, and *k*, and see different hyperbolas opening up and down. The hyperbola is graphed along with its foci, directrices, and asymptotes.