Education Technology

Introduction to Conic Sections

Published on 10/04/2011

Activity Overview

This lesson involves observing how each of the conic sections is formed and connecting the locus definition of a parabola with the vertex form of a parabola.

Objectives

  • Students will identify how each conic results from slicing cones.
  • Students will understand the locus definition of a parabola.
  • Students will describe how the values of a, h, and k in the vertex form of the equation of a parabola affect its graph.
  • Students will use the locus definition of a parabola to derive the equation of a parabola and will describe the relationships among the focus, the directrix, and the values in the vertex form of a parabola.

Vocabulary

  • circle
  • ellipse
  • parabola
  • hyperbola
  • axis of symmetry
  • focus
  • directrix

About the Lesson

This lesson involves observing how each of the conic sections is formed and connecting the locus definition of a parabola with the vertex form of a parabola.
As a result, students will:

  • Explain how each of the conic sections is formed.
  • Manipulate a point on a parabola and the focus of a parabola to discover the locus definition.
  • Manipulate a, h, and k in the vertex form of a parabola to observe the effects of each value.
  • Use the locus definition to derive the equation of a parabola given the focus, directrix, and any point on the parabola.
  • Identify the relationships among the values of the vertex form of a parabola and the focus.