1. Ch 4: The Ellipse Objectives
Use the standard and general forms of the equation of an ellipse
graph ellipses
©2002 Roy L. Gover (

2. Applications The Ellipse:
Planets travel in an elliptical path with the sun at a focus
Electrons travel in elliptical pattern about the nucleus of an atom
Applications
The Ellipse:

3. Definition
An ellipse is the locus (set) of all points such that the sum of the distances from two points called foci is constant.

4. P1(x1,y1)
Vertex
Major Axis
Minor Axis
Focus
Center

5. Important Idea An ellipse has 4 vertices
An ellipse has 2 axes-the longer is the major axis; the shorter is the minor axis
An ellipse has 2 foci located on the major axis

6. Definition
The standard form of the equation of an ellipse when the major axis is parallel to the x-axis

7. Definition c b a Center at(h,k)
An ellipse with major axis parallel to x-axis

8. Definition
The standard form of the equation of an ellipse when the major axis is parallel to the y-axis

9. Definition An ellipse with major axis parallel to y-axis a cb
Center:at (h,k) c
An ellipse with major axis parallel to y-axis

10. 2a is the length of the major axis; 2b is the length of the minor axis
Summary
The center of an ellipse is at (h,k)
2a is the length of the major axis; 2b is the length of the minor axis
c is the distance from the center to each focus

11. Important Idea
a>b a b
(h,k) c

12. Try This
Name the parts of an ellipse:

13. Try This
What letter in the standard equation represents the indicated lengths?

14. Example
For the following equation, find the coordinates of the center, foci and vertices, then graph:

15. Example
For the following equation, find the coordinates of the center, foci and vertices, then graph:

16. Important Idea
The direction of the major axis is determined by the larger denominator. The larger denominator is always a2 in the standard equation.

17. Important Idea
If the larger denominator is under the x term, the ellipse is “fat”; if the larger denominator is under the y term, the ellipse is “skinny”

18. Try This
For the following equation, find the coordinates of the center, foci and vertices, then graph:

19. Solution
Center:(0,-4)
Foci:
Vertices: (±6,-4) (0,1),(0,-9)

20. Example
For the following equation, find the coordinates of the center, foci and vertices, then graph:

21. Try This
For the following equation, find the coordinates of the center, foci and vertices, then graph:

22. Solution Center:(1,-3) Foci:(1,-3 ± ) Vertices:(0,-3),(2,-3)
(1,-1),(1,-5)

23. Lesson Close Describe the meanings of the values a, b, c, h & k.
What is wrong? a=5 ; b=6