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Exploring Geometric Constructions of Parabolas

Activity Description Activity Guide


This activity is an introduction to geometric constructions of parabolas. We will investigate their properties and characteristics. This activity has been adapted from the following article: Olmstead, E.A. (1998). Exploring the locus definition of the conic sections. Mathematics Teacher, 91(5), 428-434.

Mathematics: The students will develop geometric constructions of parabolas as loci of lines, and as loci of points. They will use the distance formula to algebraically derive the standard form of a quadratic function. Students will conjecture and prove the following theorem:

  • The distance from the parabola to its focus and the distance from the parabola to its directrix are equal.

In this activity, students will use problem-solving skills to simulate the geometric construction of a parabola using The Geometerís Sketchpad. Students will also be asked to conjecture and prove the aforementioned theorem.

Technology: This activity uses several Sketchpad commands such as: line, segment, midpoint, perpendicular line, and locus.

The following sketch illustrates a geometric construction of a parabola using The Geometerís Sketchpad.




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Last modified on August 13, 2001.