In these lessons we will learn

- about hyperbolas
- 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.

How to talk about hyperbolas.

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.

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