There is a fair amount of precalculus material on parametric equations.
We can use calculus to express the slope of the curve in terms of the
derivatives of x(t) and y(t).
In fact, by the chain rule, dy/dx = (dy/dt)/(dx/dt). This can be used to help sketch the curve and to find exact locations of 'critical points' where the tangent is horizontal or vertical.
(See, for example, this page from the University of Tennessee's Visual Calculus site )
We can also express the area inside a closed loop of the curve by means
of a definite integral.
(See Area Inside a Parametric Curve(MathCad+QT@odu) )
If you have come across good web-based illustrations of these or any other calculus applications to parametric curves, please do let us know and we will add them here.
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