Education Technology

Elimination

Published on 06/09/2008

Activity Overview

This activity uses geometric examples to illustrate the method of elimination to obtain a Cartesian equation using the Computer Algebra System CAS tool.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 6 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • In a vectorial plane, start at a certain point, and reach a certain point taking some steps of a particular vector
  • Observe the line which is generated over R
  • Recognize the fact that the parametric equations of the line are the algebraic translation of the geometric description of the line
  • Find points on the line for two values of the 'vector step'
  • Alternatively, decide whether a given point lies on the line
  • Understand that a point lies on the line if the system has a solution for the 'vector-step'
  • Verify the fact by solving the system
  • Realize that finding the Cartesian equations of a line is equivalent to finding the conditions for the coordinates of a general point in order that the system would have a solution for the 'vector-step'
  • Eliminate the step-parameter and solve the system
  • Repeat the steps by forming a plane over R when steps of two different vectors are taken to reach a point


  • Enter the equations of the circle and the line
  • Find the points of intersection and determine the equations of the two solutions
  • Draw the curve for the parametric equations
  • Eliminate the parameter 't' from the system of the associated curves, and determine the Cartesian equation of the Strophoid
  • Translate the double point of the Strophoid to the origin of the coordinate system
  • Intersect the curve with the line y = tx
  • Obtain the parametric representation for the whole strophoid
  • After the Activity

    Students understand that with the help of CAS, parameters can be eliminated directly without the use of determinants.

    Review student results.

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary