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- 1. By: Tom H. and Ashley T.Ellipses
- 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. 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. 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. 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. Real World Example 1• These stairs were built upwards in an elliptical form.
- 7. Real World Example 2• This building was built in the shape of an ellipse.
- 8. Real World Example 3• The pipe sections of this bridge are bent in the shape of an ellipse.
- 9. Nature Example 1• This egg is in the shape of an ellipse.
- 10. Nature Example 2• The Earth’s orbit around the Sun is in the shape of an ellipse.
- 11. Nature Example 3• Saturn’s rings that are composed of ice and dust are shaped like an ellipse.
- 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. 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. 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. Sources• http://tutorial.math.lamar.edu/Classes/Alg/Ell ipses.aspx#Graph_Ell_Ex1• http://www.google.com/imghp :DDD

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