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Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Find the equation, vertices, foci, axes, and asymp of a hyperbola.

Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

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Copyright © 2011 Pearson, Inc. Slide Hyperbola

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Page 1: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

8.3Hyperbolas

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

Page 2: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc. Slide 8.4 - 2

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.

Page 3: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc. Slide 8.4 - 3

Hyperbola

Page 4: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc. Slide 8.4 - 4

Hyperbola

Page 5: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

Dulles Airport

Page 6: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

Gear Transmission

Page 7: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

Sonic Boom

Page 8: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

Cooling Towers of Nuclear Reactors

Page 9: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

Page 10: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

Page 11: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

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

asymptotes.

1.

center: __________vertices: _________foci: ____________asymptotes: ______

Page 12: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

2.

center: __________vertices: _________foci: ____________asymptotes: ______

Page 13: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

3.

center: _________vertices: ________foci: ____________asymptotes: _______________

Page 14: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc. Slide 8.4 - 14

Example: Finding the Vertices and Foci of a Hyperbola

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

Page 15: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

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.

Page 16: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc.

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.

Page 17: Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola

Copyright © 2011 Pearson, Inc. Slide 8.4 - 17

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.

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