Enrichment: Mechanical Constructions of Parabolas

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 Textbook into html format.

Mechanical Constructions of Parabolas

A given line and a point determine a parabola. Here is one way to construct this curve.

Use a right triangle ABC (or stiff piece of rectangular cardboard).

Place one leg of the triangle on the given line d. Fasten one end of a string equal in length to BC at the given point F and the other end to the triangle at point B.

Put the tip of a pencil at point P and keep the string tight. The positions of F, and P must NOT be allowed to slip.

As you slide the triangle along line d, always keeping BC perpendicular to d, the point of your pencil will trace out a parabola.

At a later date in your study of mathematics, you will learn tools to derive the equations of these parabolas: given the equation of line d [the directrix] and the co-ordinates of F [the focus].