ABSTRACT

So far, we have mainly been plotting curves in parametric form. In Section 3.1, we discuss implicitly defined curves, and contrast them with those parametrized in the previous chapters. A curve is defined implicitly as the “zero set” or set of zeros of a differentiable function of two variables. In particular cases, this is the more natural way of defining the curve. Even so, if one is given the nonparametric form of a curve, it is sometimes easier to find a suitable parametrization before attempting to plot it. In any case, it can be important to be able to switch between the two representations of the curve.