5.3 Ellipse (part 2) Definition: An ellipse is the set of all points in a plane such that the sum of the distances from P to two fixed points (F1 and F2) called foci is constant.

Ellipses can have either a horizontal major axis or a vertical major axis. Note: When the bigger number is under the x term, the major axis will be on the x- axis (or parallel to it if translated). When the bigger number is under the y term, the major axis will be on the y-axis (or parallel to it if translated).

Example 4: Put the following equations in standard form for an ellipse Example 4: Put the following equations in standard form for an ellipse. State the vertices, co-vertices, and foci. Does the ellipse have a horizontal or vertical major axis?

Example 5: Sketch. Label the center, foci, vertices and co-vertices.

Example 6: Write the standard equation for an ellipse with the given characteristics. a. Foci: (5,0) and (-5, 0 ) b. Co-vertices: (0,2) and (0, -2) Vertices: (9, 0) and (-9, 0) Vertices: (3,0) and (-3, 0)

Example 7: Write a standard form equation for each ellipse Example 7: Write a standard form equation for each ellipse. Identify the center, foci, vertices, and co-vertices.

Example 7: Write a standard form equation for each ellipse Example 7: Write a standard form equation for each ellipse. Identify the center, foci, vertices, and co-vertices.

Finish Worksheet 5.3 (get graph paper if needed) Homework Finish Worksheet 5.3 (get graph paper if needed)