Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas. Copyright © 2011 Pearson, Inc. Slide 8.4 - 2 What you’ll learn about Geometry of a Hyperbola Translations.

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Presentation transcript:

Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas

Copyright © 2011 Pearson, Inc. Slide What you’ll learn about Geometry of a Hyperbola Translations of Hyperbolas Eccentricity and Orbits Reflective Property of a Hyperbola Long-Range Navigation … and why The hyperbola is the least known conic section, yet it is used astronomy, optics, and navigation.

Copyright © 2011 Pearson, Inc. Slide Hyperbola A hyperbola is the set of all points in a plane whose distances from two fixed points in the plane have a constant difference. The fixed points are the foci of the hyperbola. The line through the foci is the focal axis. The point on the focal axis midway between the foci is the center. The points where the hyperbola intersects its focal axis are the vertices of the hyperbola.

Copyright © 2011 Pearson, Inc. Slide Hyperbola

Copyright © 2011 Pearson, Inc. Slide Hyperbola

Copyright © 2011 Pearson, Inc. Slide Hyperbola with Center (0,0)

Copyright © 2011 Pearson, Inc. Slide Hyperbola Centered at (0,0)

Copyright © 2011 Pearson, Inc. Slide Example Finding the Vertices and Foci of a Hyperbola

Copyright © 2011 Pearson, Inc. Slide Example Finding the Vertices and Foci of a Hyperbola

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

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

Copyright © 2011 Pearson, Inc. Slide Hyperbola with Center (h,k)

Copyright © 2011 Pearson, Inc. Slide Hyperbola with Center (h,k)

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

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

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

Copyright © 2011 Pearson, Inc. Slide Example Locating Key Points of a Hyperbola

Copyright © 2011 Pearson, Inc. Slide Example Locating Key Points of a Hyperbola

Copyright © 2011 Pearson, Inc. Slide Eccentricity of a Hyperbola

Copyright © 2011 Pearson, Inc. Slide Quick Review

Copyright © 2011 Pearson, Inc. Slide Quick Review Solutions