Precalculus: Polar Conics

Objectives

• Students will understand that the equations for conics can be expressed in polar form.
• Students will be able to describe the relationship between eccentricity and the type of conic section.
• Students will be able to describe the relationship between distance from the conic to the directrix and the graph of the conic section.
• Students will be able to describe the effects of a phase shift in the polar form of an equation for a conic on the graph of the conic.

Vocabulary

• polar form
• conic
• parabola
• ellipse
• hyperbola
• directrix
• eccentricity
• phase shift

About the Lesson

This lesson involves exploration of polar equations for conic sections.
As a result, students will:

• Manipulate the parameters of polar equations for conics and observe the results.
• Investigate the parameters required to produce a specified conic.