The document defines key terms and properties of ellipses including their major and minor axes, vertices, foci, and a formula to calculate the distance between the center and foci. It then provides examples of specific ellipses, calculating their major and minor axis lengths and locating their centers and foci.

1. Ellipse facts
Major axis (longer)
Minor axis (shorter)
Vertices and foci lie on the major axis
Center is at the intersection of the axes
Length of major axis = 2a
Length of minor axis = 2b
Foci are a distance of c from the center, where
c = a2 - b2

2. longer axis horizontal longer axis vertical

3. Write an equation for the ellipse shown.
a=5
b=3
Major axis is vertical

4. Center: (0, 0) Graph the
ellipse and its
foci:
Major axis is horizontal
Length of the major axis: 12
Length of the minor axis: 6
Foci:
c2 = a2 - b2
c2 = 36 - 9
c2 = 27
c=

5. 2
36 36 36

6. Center: (3, 2)
Major axis is horizontal
Length of the major axis: 12
Length of the minor axis: 6
Foci:
c2 = a2 - b2
c2 = 36 - 9
c2 = 27
c=