Education Technology

# Activities

• ##### Subject Area

• Math: Precalculus: Analytic Geometry (Conics)

9-12

45 Minutes

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

TI-Nspire™ CX
TI-Nspire™ CX CAS

5.0

## 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