# 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.

Hyperbolas