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

2. Copyright © 2011 Pearson, Inc. Slide 8.4 - 2 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.

3. Copyright © 2011 Pearson, Inc. Slide 8.4 - 3 Hyperbola

4. Copyright © 2011 Pearson, Inc. Slide 8.4 - 4 Hyperbola

5. Copyright © 2011 Pearson, Inc. Dulles Airport

6. Copyright © 2011 Pearson, Inc. Gear Transmission

7. Copyright © 2011 Pearson, Inc. Sonic Boom

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

9. Copyright © 2011 Pearson, Inc.

11. Graph the hyperbolas. Indicate the coordinates of the center, vertices, and foci. Give the equations of the asymptotes. 1. center: __________ vertices: _________ foci: ____________ asymptotes: ______

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

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

14. Copyright © 2011 Pearson, Inc. Slide 8.4 - 14 Example: Finding the Vertices and Foci of a Hyperbola

15. 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.

16. 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.

17. Copyright © 2011 Pearson, Inc. Slide 8.4 - 17 Example: Finding an Equation of a Hyperbola