Ellipses by Tom & Ashley

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Ellipses by Tom & Ashley

  1. 1. By: Tom H. and Ashley T.Ellipses
  2. 2. Definition• A regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane that does not intersect the base.• The standard form of an ellipse is:
  3. 3. Example 1• The equation of this first ellipse is:• The center of this ellipse is (-2,4).• a = 3 and b = 5 – Right most point: (1,4) – Left most point: (-5,4) – Top most point: (-2,9) – Bottom most point: (-2,-1)
  4. 4. Example 2• The equation of the second ellipse is:• The center of this ellipse is (0,3).• a = 7 and b = 2 – Right most point: (7,3) – Left most point: (-7,3) – Top most point: (0,5) – Bottom most point: (0,1)
  5. 5. Example 3• The equation of the third ellipse is:• The center of this ellipse is (-1,-3).• a = ½ and b = 1 – Right most point: (-½,-3) – Left most point: (-3/2,-3) – Top most point: (-1,-2) – Bottom most point: (-1,-4)
  6. 6. Real World Example 1• These stairs were built upwards in an elliptical form.
  7. 7. Real World Example 2• This building was built in the shape of an ellipse.
  8. 8. Real World Example 3• The pipe sections of this bridge are bent in the shape of an ellipse.
  9. 9. Nature Example 1• This egg is in the shape of an ellipse.
  10. 10. Nature Example 2• The Earth’s orbit around the Sun is in the shape of an ellipse.
  11. 11. Nature Example 3• Saturn’s rings that are composed of ice and dust are shaped like an ellipse.
  12. 12. Graph Example 1• The equation from Example 1 was: – Right most point: (1,4) – Left most point: (-5,4) – Top most point: (-2,9) – Bottom most point: (-2,-1)
  13. 13. Graph Example 2• The equation from Example 2 was: – Right most point: (7,3) – Left most point: (-7,3) – Top most point: (0,5) – Bottom most point: (0,1)
  14. 14. Graph Example 3• The equation from Example 3 was: – Right most point: (-½,-3) – Left most point: (-3/2,-3) – Top most point: (-1,-2) – Bottom most point: (-1,-4)
  15. 15. Sources• http://tutorial.math.lamar.edu/Classes/Alg/Ell ipses.aspx#Graph_Ell_Ex1• http://www.google.com/imghp :DDD

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