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.
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)