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8.1

Goal: Find the equation, focus, and directrix of a parabola. 8.1. Parabolas. What you’ll learn about. Geometry of a Parabola Translations of Parabolas Reflective Property of a Parabola … and why Conic sections are the paths of nature: Any free-moving

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8.1

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  1. Goal: Find the equation, focus, and directrix of a parabola. 8.1 Parabolas

  2. What you’ll learn about • Geometry of a Parabola • Translations of Parabolas • Reflective Property of a Parabola … and why Conic sections are the paths of nature: Any free-moving object in a gravitational field follows the path of a conic section.

  3. Golden Arches

  4. Satellite Dishes Incoming Waves are concentrated to the focus.

  5. Heaters Heaters are sold which make use of the reflective property of the parabola. The heat source is at the focus and heat is concentrated in parallel rays. Have you walked by the parabolic reflector heater at COSTCO?

  6. Path of a Ball Gallileo was the first to show that the path of an object thrown in space is a parabola.

  7. Suspension Cables on the Golden Gate Bridge

  8. Parabola A parabola is the set of all points in a plane equidistant from a particular line (the directrix) and a particular point (the focus) in the plane.

  9. Graphs of x2 = 4py

  10. Graphs of y2 = 4px

  11. For each parabola, find the vertex, focus, directrix, and focal chord length then sketch. vertex: ____________ focus: _____________ directrix: _________ focal chord: _________

  12. vertex: ____________ focus: _____________ directrix: _________ focal chord: _________

  13. vertex: ____________ focus: _____________ directrix: _________ focal chord: __________

  14. vertex: ____________ focus: _____________ directrix: _________ focal chord: __________

  15. vertex: ____________ focus: _____________ directrix: ________ focal chord: ________

  16. Find the equation of the parabola and sketch its graph. Vertex at (0, 0) and directrix of x = 5.

  17. Find the equation of the parabola and sketch its graph. Focus at (3, -2) and directrix of y = 4.

  18. Find the vertex, focus, and length of the focal chord for the parabola below. vertex: _____________ focus: ______________ focal chord: __________

  19. Example Finding an Equation of a Parabola

  20. Example Finding an Equation of a Parabola

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