1. Demana, Waits, Foley, Kennedy
8.2
Circles and Ellipses

2. What you’ll learn about
Transforming the Unit Circle
Geometry of an Ellipse
Translations of Ellipses
Orbits and Eccentricity
Reflective Property of an Ellipse
… and why
Ellipses are the paths of planets and comets around the
Sun, or of moons around planets.

3. Ellipse
An ellipse is the set of all points in a plane whose distance from two fixed points in the plane have a constant sum. The fixed points are the foci (plural of focus) of the ellipse. The line through the foci is the focal axis. The point on the focal axis midway between the foci is the center. The points where the ellipse intersects its axis are the vertices of the ellipse.

4. Key Points on the Focal Axis of an Ellipse

5. Pythagorean Relation

6. Ellipse with Center (0,0)

9. Example: Finding the Vertices and Foci of an Ellipse

10. Solution

11. Example: Finding an Equation of an Ellipse

12. Solution

15. Ellipse with Center (h,k)

16. Ellipse with Center (h,k)

17. Example: Finding an Equation of an Ellipse

18. Solution

19. Solution Continued

20. Example: Locating Key Points of an Ellipse

21. Solution

22. Elliptical Orbits Around the Sun

23. Eccentricity of an Ellipse