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Ellipses

By: Tom H. and Ashley T. Ellipses. 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.

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Ellipses

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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/Ellipses.aspx#Graph_Ell_Ex1 • http://www.google.com/imghp :DDD

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