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

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Presentation transcript:

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

Copyright © 2011 Pearson, Inc. Slide What you’ll learn about Geometry of a Hyperbola … and why The hyperbola is the least known conic section, yet it is used astronomy, optics, and navigation.

Copyright © 2011 Pearson, Inc. Slide Hyperbola

Copyright © 2011 Pearson, Inc. Slide Hyperbola

Copyright © 2011 Pearson, Inc. Dulles Airport

Copyright © 2011 Pearson, Inc. Gear Transmission

Copyright © 2011 Pearson, Inc. Sonic Boom

Copyright © 2011 Pearson, Inc. Cooling Towers of Nuclear Reactors

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: ______

Copyright © 2011 Pearson, Inc. 2. center: __________ vertices: _________ foci: ____________ asymptotes: ______

Copyright © 2011 Pearson, Inc. center: _________ vertices: ________ foci: ____________ asymptotes: _______________

Copyright © 2011 Pearson, Inc. Slide Example: Finding the Vertices and Foci 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.

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.

Copyright © 2011 Pearson, Inc. Slide Example: Finding an Equation of a Hyperbola