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4x;<V}FUsing Sketchpad in Calculus - 2. Doris Schattschneider
Parametric equations of curves is a main topic in calculus (usually the second semester). Many of the curves for which parametric equations are sought are generated as loci of moving points that are constructed geometrically. The cycloid is a well-known example treated in most calculus texts. Our text, Stewart's "Calculus," treats this in section 9.1. At the end of that section are several problems in which a sketch of a geometrically constructed point is given and the student is asked to find the parametric equations of the locus of the point, and also sketch the locus.
The sketch for problem 40 is given above. The curve generated by P when point B is animated on the line x = 2a is called the "cissoid of Diocles". It is helpful to generate the curve with Sketchpad as well as discover the constraints on how far B must travel to sweep out the whole curve. The student must still find the parametric equations for the locus of P as B travels back and forth on the line. nd the parametric equations for the locus of P as the ray OQ sweeps around the circle, where thehU 1
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