The document defines an ellipse as an oval shape traced by a point moving in a plane such that the sum of its distances from two focal points is constant. It provides three examples of ellipse equations with their center and extreme points identified. Real-world, natural, and graphical examples of ellipses are given, including staircases, buildings, bridge pipes, eggs, planetary orbits, and Saturn's rings.

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