Lesson 2: 9.2 Ellipses
Duration of Days: 4
Lesson Objective
1. Write equations of ellipses in standard form.
2. Use properties of ellipses to model and solve real-life problems.
3. Find eccentricities of ellipses.
How do you solve problems involving ellipses?
ellipse
foci
vertices
major axis
minor axis
eccentricity
HSG-GPE.A.3 - Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
Use Khan Academy Resources
Students will expand on their knowledge of the conic sections to learn about the graph and characteristics of an ellipse, which will be applied to the study of astronomy.
Ellipses can be used to model and solve many types of real-life problems. Focal properties of an ellipse are used by a lithotripter to break up kidney stones.
Remind students that they must complete the square for both variables when writing the equation in standard form.
When the equation of an ellipse is in standard form, encourage students to look for the term with the larger denominator in order to determine the direction of the major axis.
When discussing ellipses, you might also choose to discuss the latera recta as background.
To ensure an accurate graph of an ellipse, encourage students to plot the endpoints of the minor axis in addition to the center and vertices.
Use Common Assessments
Pre-Calculus with Limits