Parametric Curve

Parametric equations can be used to represent curves whose graphs are not simple functions of the type y = f(x), where y and x are represented along the vertical and horizontal axes, respectively. Instead, the curves in the x-y plane are defined parametrically as two simultaneous functions of a parameter t that ranges over some interval (minimum, maximum). You can specify an equation y = f(t) for the y-component of the curve, and an equation x = g(t) for the x-component of the curve, for a specified range of parameter t.  

Options for specifying and plotting parametric curves are available on the Custom Function (2D Graphs) tab of the 2D graph Graph Options dialog box; you can also specify plots of parametric curves via the 2D Custom Function Plots options. These options make it possible for you to plot curves and functions that cannot be expressed in a simple fit of type y = f(x).

For example, to plot a spiral, you could specify:

y(t) = t*cos(t)

x(t) = t*sin(t)

For 0 < = t < = 12.

There are a wide variety of curves, from simple circles to complex shapes that can be produced via the parametric curves facilities. Here is another example:

y(t) = (a + b)*sin(t) - b*sin((a/b + 1)*t)

x(t) = (a + b)*cos(t) - b*cos((a/b + 1)* t)

In the plot shown above, a and b were set to 8 and 5, respectively, and parameter t was plotted over the range from 0 to 100. If you change a and b in the parametric equations shown above, very different shapes will emerge.