Education Technology

Foci Definition of Ellipses and Hyperbolas

Activity Overview

This lesson involves observing and describing the relationships between the foci of ellipses and hyperbolas and the shape of the corresponding curves.

Objectives

  • Students will be able to define an ellipse as the set of points whose distances to two fixed points (foci) have a constant sum.
  • Students will be able to define a hyperbola as the set of points whose distances to two fixed points (foci) have a constant difference.
  • Students will be able to describe the relationship between the location of the foci and the shapes of the corresponding ellipses and hyperbolas.
  • Students will be able to determine the effect of the eccentricity of ellipses and hyperbolas on the shape of their curves.

Vocabulary

  • conjugate axis
  • eccentricity
  • ellipse
  • focus/foci
  • hyperbola
  • major axis
  • minor axis
  • semi-major axis
  • semi-minor axis
  • transverse axis
  • vertex of a conic

About the Lesson

This lesson involves observing and describing the relationships between the foci of ellipses and hyperbolas and the shape of the corresponding curves.
As a result, students will:

  • Define an ellipse as the set of points whose distances to two fixed points (foci) have a constant sum.
  • Define a hyperbola as the set of points whose distances to two fixed points (foci) have a constant difference.
  • Manipulate sliders to observe the relationship between the foci and sum/difference of the distances from the foci to a point on the curve.
  • Observe the effect of the relationship between the foci and the shapes of ellipses or hyperbolas.