 # Hyperbolas

A series of free, online Intermediate Algebra Lessons or Algebra II lessons.

In these lessons we will learn

• transformations of hyperbolas
• how to identify conic sections by their formulas or equations

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Videos, worksheets, and activities to help Algebra students.

### The Hyperbola

A hyperbola is a type of conic section that is formed by intersecting a cone with a plane, resulting in two parabolic shaped pieces that open either up and down or right and left. Similar to a parabola, the hyperbola pieces have vertices and are asymptotic. The hyperbola is the least common of the conic sections.
Conic Sections: The Hyperbola part 1 of 2
This video defines a hyperbola and explains how to graph a hyperbola given in standard form.

Conic Sections: The Hyperbola part 2 of 2
This video explains how to graph a hyberbola in general form.

### Transformations of a Hyperbola:

Hyperbola Graphs Graphing a transformed hyperbola combines the skills of graphing hyperbolas and graphing transformations. With hyperbola graphs, we use the formula a^2 + b^2 = c^2 to determine the foci and y= + or - (a/b)x to determine the asymptotes. When transforming hyperbola graphs, we find the center of the graph and then graph accordingly.
How to transform the graph of a hyperbola.

This video shows how to sketch the graph of a shifted hyperbola.

### Conic Section Formulas

We can easily identify a conic section by its formula. Conic section formulas have different identifiers. For example, a vertical parabola has a squared "x" term and single "y" term while a horizontal parabola has a single "x" term and a "y" squared term. An equation for a circle has a squared "x" term, a squared "y" term and identical coefficients.
How to identify a conic section by its formula.

This video explains how to determine if a given equation in general form is a circle, ellipse, parabola, or hyperbola.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  