Education Technology

Precalculus: Foci Definition of Ellipses and Hyperbolas
by Texas Instruments

Published on October 03, 2011

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.