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8.3Hyperbolas
Goal: Find the equation, vertices, foci, axes, and asymptotes of a hyperbola.
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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.
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Copyright © 2011 Pearson, Inc. Slide 8.4 - 3
Hyperbola
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Copyright © 2011 Pearson, Inc. Slide 8.4 - 4
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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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.
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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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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.