1. Ellipses Objective: Be able to get the equation of an ellipse from given information or the graph Be able to find the key features of and graph an ellipse Thinking Skill: Explicitly assess information and draw conclusions Warm Up: Sketch the ellipse. Also list/recall all you remember about ellipses in general

2. Ellipse Definition: An ellipse is the set of all points (x, y) where the sum of the distances from two fixed points (foci) is constant Equations –Horizontal – Vertical Where the center is (h, k), 2a is the major axis length, 2b is the minor axis length, and c 2 = a 2 – b 2 And the eccentricity e=c/a, where 0 < e < 1

3. Examples Find the center, vertices, foci, co-vertices and eccentricity of then graph.

4. Examples Find the center, vertices, foci, co-vertices and eccentricity then graph

5. Examples Find the equation of the ellipse with foci (2, 0) and (-2,0) and whose major axis is 8 units.

6. Examples Find the equation of the ellipse with vertices (3, -2) and (3, -8) and whose minor axis is 4 units long.

7. Examples Find the equation of the ellipse with vertices (0, 8) and (0, -8) and whose eccentricity is 1/2.

8. Graphing them in the calculator. How could I graph the below ellipse in my calculator?