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Examples on Parametric Equations

Example 1

Find two parametric representations (one clockwise, one counter clockwise) for the ellipse whose equation is given below.

 

Click on each parameterization to see an animation

 

 

 

 

 

Example 2

 

Determine the values of t for which the graph of the curve (inverted cycloid) represented parametrically below is not smooth.

 

 

Example 3

 

Determine the values of t for which the graph of the curve (epicycloid) represented parametrically below is not smooth.  Click here to see an animated point moving along the curve.  Notice how it seems to momentarily stop at each point where the curve is not smooth.

 

 

Example 4

Give a parametric representation of the hyperbola whose equation is given below.

 

 

 

 

 

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        Lane Vosbury, Mathematics, Seminole State College   email:  vosburyl@seminolestate.edu

        This page was last updated on 08/21/14          Copyright 2002          webstats