1. What is The equation of an Ellipse

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

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

4. Definition c b a Center at(h,k)
An ellipse with a horizontal major axis.

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

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

7. Definition An ellipse with a vertical major axis. a c Center:at (h,k)b
Center:at (h,k) c

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

9. 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”
The direction of the major axis is determined by the larger denominator. The larger denominator is always a2 in the standard equation.

10. Try This
For the following ellipse, find the coordinates of the center, foci, vertices, & endpoints of the minor axis. Then graph.

11. Solution Center:(0,-4) Foci:
Vertices: (±6,-4) Minor Axes Ends(0,1),(0,-9)

12. Try This
Write an equation of the ellipse with Foci (3,2) and (3,-4) and whose major axes is 14 units long.

13. Solution

14. How is the “roundness” of an
ellipse measured?

15. Try This
For the following ellipse, find the coordinates of the center, foci, vertices, & endpoints of the minor axis. Then graph.

16. Solution Center:(2,-3) Foci:
Vertices: (6,-3) (-2,-3) Minor Axes Ends(2,-6),(2,0)

17. Quick Summary Describe the meanings of the values a, b, c, h & k.
What is wrong? a=5 ; b=6