This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# ParametricPlot

 ParametricPlot[{fx, fy}, {u, umin, umax}]generates a parametric plot of a curve with x and y coordinates fx and fy as a function of u. ParametricPlot[{{fx, fy}, {gx, gy}, ...}, {u, umin, umax}]plots several parametric curves. ParametricPlot[{fx, fy}, {u, umin, umax}, {v, vmin, vmax}]plots a parametric region. ParametricPlot[{{fx, fy}, {gx, gy}, ...}, {u, umin, umax}, {v, vmin, vmax}]plots several parametric regions.
• ParametricPlot has attribute HoldAll, and evaluates the fi and gi only after assigning specific numerical values to variables.
• In some cases it may be more efficient to use Evaluate to evaluate the fi and gi symbolically before specific numerical values are assigned to variables.
• No curve is drawn in any regions where the corresponding fi or gi evaluate to None.
 AspectRatio Automatic ratio of height to width Axes True whether to draw axes BoundaryStyle Automatic how to draw boundaries of regions ColorFunction Automatic how to apply coloring to curves or regions ColorFunctionScaling True whether to scale arguments to ColorFunction EvaluationMonitor None expression to evaluate at every function evaluation Exclusions Automatic u points or u, v curves to exclude ExclusionsStyle None what to draw at excluded points or curves Frame Automatic whether to put a frame around the plot MaxRecursion Automatic the maximum number of recursive subdivisions allowed Mesh Automatic how many mesh divisions to draw MeshFunctions Automatic how to determine the placement of mesh divisions MeshShading None how to shade regions between mesh points or lines MeshStyle Automatic the style for mesh divisions Method Automatic the method to use for refining curves or regions PerformanceGoal \$PerformanceGoal aspects of performance to try to optimize PlotPoints Automatic initial number of sample points in each parameter PlotRange Automatic range of values to include PlotRangeClipping True whether to clip at the plot range PlotStyle Automatic graphics directives to specify the style for each object RegionFunction (True&) how to determine whether a point should be included WorkingPrecision MachinePrecision the precision used in internal computations
• ParametricPlot[Tooltip[{{fx, fy}, ...}, ...]] specifies that {fx, fy} should be displayed as tooltip labels for the corresponding curves or regions.
• Tooltip[{fx, fy}, label] specifies an explicit tooltip label for a curve or region.
• ParametricPlot initially evaluates each function at a number of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to choose additional sample points, subdividing a given interval in each parameter at most MaxRecursion times.
• You should realize that with the finite number of sample points used, it is possible for ParametricPlot to miss features in your functions. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.
• On[ParametricPlot::accbend] makes ParametricPlot print a message if it is unable to reach a certain smoothness of curve.
• The default setting corresponds to None for curves, and 15 for regions.
• With Mesh->All, ParametricPlot will explicitly draw a point at each sample point on each curve, or will draw a line to indicate each region subdivision.
• The default setting corresponds to {#3&} for curves, and {#3&, #4&} for regions.
• The functions are evaluated all along each curve, or all over each region.
Plot a parametric curve:
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Plot a parametric region:
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Plot several parametric curves:
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Plot overlapping regions:
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 Scope   (14)
 Options   (61)
 Applications   (9)