Precalculus: Focus/Directrix Definition of Conics

Objectives

• Students will describe the relationship between the focus and the directrix associated with three types of conics.
• Students will define parabolas, ellipses, and hyperbolas by their focus and directrix.

Vocabulary

• parabola
• ellipse
• hyperbola
• focus
• directrix

About the Lesson

This lesson involves observing and describing relationships between the focus and the directrix of each conic: parabolas, ellipses, and hyperbolas.
As a result, students will:

• Manipulate the focus and the directrix of a conic to observe the relationships between the focus, the directrix, and the conic.
• Observe the effect of the relationship between the focus and the directrix on the shape of an ellipse or hyperbola.
• Define a parabola, an ellipse, and a hyperbola, by their respective focus and directrix.