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