copyright © 2011 pearson, inc. 8.3 hyperbolas goal: find the equation, vertices, foci, axes, and...

Copyright © 2011 Pearson, Inc.

8.3Hyperbolas

Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola.

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What you’ll learn about

Geometry of a Hyperbola

… and whyThe hyperbola is the least known conic section, yet it is used astronomy, optics, and navigation.

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Hyperbola

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Hyperbola

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Dulles Airport

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Gear Transmission

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Sonic Boom

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Cooling Towers of Nuclear Reactors

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Graph the hyperbolas. Indicate the coordinates of the center, vertices, and foci. Give the equations of the

asymptotes.

1.

center: __________vertices: _________foci: ____________asymptotes: ______

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2.

center: __________vertices: _________foci: ____________asymptotes: ______

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3.

center: _________vertices: ________foci: ____________asymptotes: _______________

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Example: Finding the Vertices and Foci of a Hyperbola

Find the vertices and the foci of the hyperbola9x2 4y2 36.

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Example: Finding the Vertices and Foci of a Hyperbola

Find the vertices and foci of the hyperbola by first rewriting the hyperbola in its standard form.

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Example: Finding an Equation of a Hyperbola

A hyperbola has a center at (2, 4) and an asymptote of y = 2x. Find the equation of the hyperbola given it has a horizontal transverse axis of length 12.

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Example: Finding an Equation of a Hyperbola

Find an equation of the hyperbola with foci (0,4) and(0, 4) whose conjugate axis has length 2.