Education Technology

# Activities

• ##### Subject Area

• Math: Precalculus: Analytic Geometry (Conics)

9-12

45 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• TI-84 Plus C Silver Edition
• TI-84 Plus CE

## Properties of an Ellipse

#### Activity Overview

Students discover properties of an ellipse, such as the set of all points such that the sum of the distances from these points to two fixed points is constant.

#### Key Steps

• Students investigate the definition of an ellipse. They graph an ellipse, trace the graph, and record the coordinates of at least ten points.

• Students pick two of the points from the table on the previous page.

Using the given coordinates for the foci, students find the distance between the points picked and each focus point. From their observations students form their own definition of an ellipse.

• Students form a relationship between the foci and point P by drawing a vector from one focus point to P and from P to the second focus.