# Activities

• • • ##### Subject Area

• Math: Precalculus: Analytic Geometry (Conics)

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.0

• ##### Report an Issue

Elliptic Variations

#### Activity Overview

This lesson involves exploring the curves that result from varying the defining conditions of an ellipse.

#### 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.

• 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.