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Hyperbolas

Precalculus. Lesson 8.3. Hyperbolas. Quick Review. Quick Review. No Solution since it can never equal zero. 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

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Hyperbolas

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  1. Precalculus Lesson 8.3 Hyperbolas

  2. Quick Review

  3. Quick Review No Solution since it can never equal zero

  4. 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.

  5. 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.

  6. Hyperbola with Center (0,0)

  7. Hyperbola with Center (0,0)

  8. Example Finding the Vertices and Foci of an Hyperbola

  9. Example Finding an Equation of an Hyperbola

  10. Hyperbola with Center (h,k)

  11. Hyperbola with Center (h,k)

  12. Example Locating Key Points of a Hyperbola

  13. Eccentricity of an Hyperbola

  14. Homework: Text pg663/664 Exercises # 2-42 (intervals of 4) And #52

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