EJMT Abstract

The locus problems discussed in this paper are inspired by college entrance exam practice problems from China. Finding the algebraic equations for the locus that depends on other curves may not be a simple task. However, it will become more intuitive to students if we use a dynamic geometry software (DGS) to trace graphically what the locus may look like first before verifying the equation analytically with a computer algebra system (CAS). In addition to finding the locus for a given problem, we shall generate families of new parametric locus curves from the existing closed curve.

In many places, we first highlight essential algebraic manipulation skills before we explore various scenarios when technological tools are available to learners. The activities described in this paper are accessible to student who have knowledge of parametric equations.