Precalculus: Elliptic Variations

Objectives

• Students will be able to describe the characteristics of the graphs of equations of the form |(x/a)|ⁿ + |(y/b)|ⁿ = 1 for various values of n.
• Students will be able to describe the characteristics of the graphs of equations of the form √((x-a)²+y²)*√((x+a)²+y²) = b² when a = 4 and b varies.

Vocabulary

• ellipse
• superellipse
• Cassini oval

About the Lesson

This lesson involves exploring the curves that result from varying the defining conditions of an ellipse.
As a result, students will:

• Analyze the properties of the graphs and equations of superellipses and Cassini ovals.
• Analyze the derivations of the parametric representation of a superellipse and the polar representation of a Cassini oval.