Education Technology

Constructing an Ellipse

Activity Overview

Students will explore two different methods for constructing an ellipse. Students discover that the sum of the distances from a point on an ellipse to its foci is always constant. This fact is then used as the basis for an algebraic derivation of the general equation for an ellipse centered at the origin.

Key Steps

  • Image

    Students should begin by examining the circle on page 1.3. They will see that point F lies on a diameter of the circle, segment FP connects F to a point P on the circle, and a perpendicular line to segment FP through point P is drawn.

    Students are directed to drag point P around the circle and then display the locus (MENU > Construction > Locus) of the perpendicular line as P travels along the circle, which generates the shape of an ellipse.