1. 6-3 Ellipses
Objectives:
1. Graph ellipses.
2. Find equations of ellipses.

2. Definition of an Ellipse
 Set of all points P such that the sum
of the distances between P and the
two foci (plural for “focus”) is
constant.
d1 + d2 = constant

3. Horizontal
Major Axis:

4. Vertical Major
Axis:

5. Finding Foci
The foci are on the major axis,
c units from the center,
where c2 = a2 – b2
Remember a > b

6. Graphing Ellipses
1. Write in standard form.
2. Use a and b to plot vertices and
co-vertices.
3. Sketch the ellipse.

7. Example:
 Sketch the ellipse and identify
the foci.

8. You Try!
Graph and identify the foci.

9. Writing Equations
Write an equation of the ellipse
with the given characteristics and
center (0, 0).
Vertex: (0, 7)
Minor axis 12 units long
Vertex: (-4, 0)
Focus: (2, 0)

10. You Try!
Write an equation of the ellipse
with center (0,0), vertex at (0, 4)
and minor axis 4 units long.
Find the coordinates of the foci.