1. Graph and Write Equations of Elllipses
Section 9.4
Graph and Write Equations of Elllipses

2. California Standard:
16.0: Students demonstrate and explain how the geometry of the graph of a conic section depends on the coefficients of the quadratic equation representing it.

3. By following instructions, students will be able to:
OBJECTIVE(S):
By following instructions, students will be able to:
Graph and write equations of ellipses.

4. Def: An ellipse is the set of all points P in a plane such that the sum of the distances between P and two fixed points, called the foci, is a constant Standard Equation of an Ellipse with Center at the Origin y y x x

5. EXAMPLE 1:
Graph Identify the vertices, co-vertices and foci of the ellipse.

6. U-TRY#1:
Graph the equation. Identify the vertices, co-vertices, and foci of the ellipses. A) B) C)

7. EXAMPLE 2:
Write an equation of the ellipse that has a vertex at (0,4), a co-vertex at (-3,0), and center at (0,0).

8. EXAMPLE 3:
Write an equation of an ellipse that has a major horizontal axis of 400 and a minor vertical axis of 200.

9. EXAMPLE 4:
Write an equation of the ellipse that has a vertex at (- 8,0), a focus at (4,0), and center at (0,0).

10. U-TRY#2:
Write an equation of the ellipse with the given characteristics and center at (0,0)
Vertex: (7,0); co-vertex: (0,2)
Vertex: (0,6); co-vertex (-5,0)
Vertex: (0,8); focus: (0,-3)
Vertex: (-5,0); focus: (3,0)

11. HOMEWORK
Sec 9.4 WS