Precalculus: Reflective Property of Conics

Objectives

• Students will be able to state the reflection property for a flat surface in terms of the equality of angle of incidence and angle of reflection and apply it to a curved surface (using the tangent line as a flat surface).
• Students will be able to describe the special distance relationships satisfied by any point on each of the three conic sections (parabola, ellipse, and hyperbola) in terms of their foci and/or directrix.
• Students will be able to describe the reflective (carom) properties of each of the three conic sections (parabola, ellipse, and hyperbola) in terms of their foci and/or directrix.

Vocabulary

• conic sections (parabola, ellipse, hyperbola)
• tangent line
• angle of incidence
• angle of reflection

About the Lesson

This lesson involves investigating the properties of basic reflective principles of conics.
As a result, students will:

• Manipulate the source of the ray and its point of contact with the conic to observe its effect on the reflected ray.
• See the special reflective properties of each conic in terms of foci and/or directrix.
• Consider applications of the reflective properties.