1. Copyright © 2011 Pearson, Inc. 8.3 Hyperbolas

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

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

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

5. Copyright © 2011 Pearson, Inc. Slide 8.4 - 5 Hyperbola

6. Copyright © 2011 Pearson, Inc. Slide 8.4 - 6 Hyperbola with Center (0,0)

7. Copyright © 2011 Pearson, Inc. Slide 8.4 - 7 Hyperbola Centered at (0,0)

8. Copyright © 2011 Pearson, Inc. Slide 8.4 - 8 Example Finding the Vertices and Foci of a Hyperbola

9. Copyright © 2011 Pearson, Inc. Slide 8.4 - 9 Example Finding the Vertices and Foci of a Hyperbola

10. Copyright © 2011 Pearson, Inc. Slide 8.4 - 10 Example Finding an Equation of a Hyperbola

11. Copyright © 2011 Pearson, Inc. Slide 8.4 - 11 Example Finding an Equation of a Hyperbola

12. Copyright © 2011 Pearson, Inc. Slide 8.4 - 12 Hyperbola with Center (h,k)

13. Copyright © 2011 Pearson, Inc. Slide 8.4 - 13 Hyperbola with Center (h,k)

14. Copyright © 2011 Pearson, Inc. Slide 8.4 - 14 Example Finding an Equation of a Hyperbola

15. Copyright © 2011 Pearson, Inc. Slide 8.4 - 15 Example Finding an Equation of a Hyperbola

16. Copyright © 2011 Pearson, Inc. Slide 8.4 - 16 Example Finding an Equation of a Hyperbola

17. Copyright © 2011 Pearson, Inc. Slide 8.4 - 17 Example Locating Key Points of a Hyperbola

18. Copyright © 2011 Pearson, Inc. Slide 8.4 - 18 Example Locating Key Points of a Hyperbola

19. Copyright © 2011 Pearson, Inc. Slide 8.4 - 19 Eccentricity of a Hyperbola

20. Copyright © 2011 Pearson, Inc. Slide 8.4 - 20 Quick Review

21. Copyright © 2011 Pearson, Inc. Slide 8.4 - 21 Quick Review Solutions