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10.4 Ellipses Inked
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10.4 Ellipses Inked

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  • 1. 10.4 Ellipses
  • 2. http://www.mathwarehouse.com/ellipse/eccentricity-orbiting-planets.php An Ellipse is:
  • 3. Construct an ellipse
    • Turn your notes over. On the back, draw two points 2 – 3” apart.
    • Find someone to work with.
    • Have your partner put the knots of the string on the points and hold them down.
    • Pull the string taut with a pencil and slide the pencil to draw the ellipse.
    http:// mathworld.wolfram.com/Ellipse.html
  • 4. The location of each tack is called a focus, because one of the properties possessed by an ellipse: light rays emanating from a source at one focus and reflected by the ellipse would all return to the other focus. This we prove by recalling a physical property of light: it always travels by the shortest available path.
  • 5.  
  • 6.  
  • 7. This reflecting property of the ellipse explains the sound effects obtained in certain so-called whispering galleries. If you and your friend stand close to and facing the wall, at opposite corners of the intersection of the two ramps, as at A and B in Figure 21, you can talk in very subdued tones and hear each other perfectly, while people passing between you will be unable to hear your conversation. You are standing at the two foci of an elliptical part of the ceiling.
  • 8.  
  • 9. Cincinnati’s Union Terminal
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  • 13.  
  • 14. Example 1. Write the equation of an ellipse with center of (0, 0), vertex at (0, 5), and co-vertex at (2, 0).
  • 15. Example 2 . Write the equation of the ellipse with center (-2, 1), horizontal major axis of length 6 and minor axis of length 4.
  • 16.  
  • 17.  
  • 18. Example 5 . Write each ellipse in standard form. Then find its center, vertices, and foci.
    • 25x 2 + 9y 2 = 225
    • 3x 2 + 6x + y 2 – 6y = -3
  • 19. Your assignment is. . .
    • A worksheet!