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In this paper, we will consider several one-parameter families of plane curves bounding a constant area in the first quadrant. At the beginning, we will consider one-parameter families of straight lines, parabolas, and ellipses. The envelopes of these families are of significant interest. We will use the computer algebra system Mathematica to make certain conjectures regarding these envelopes. We will also show how to use Mathematica to create animations to illustrate the behavior of the above curves as the parameter changes. Finally, we consider more general types of one-parameter families of curves bounding a constant area. The computer algebra systems have completely changed the way we teach and think about mathematics. This paper will illustrate the great impact of the computer algebra systems on the teaching and learning of mathematics.
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