Education Technology

Elliptic Variations

Published on 09/24/2011

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.

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.