Plotting a parametric curve in the plane

We work out an example of a parametric curve in the plane given in class

First we define a parametric curve in the plane via the function F:

In[1]:=

F[t_] := {t/(t^2 + 1), 1/(t^2 + 1)}

The following command plots our parametric curve for -10<=t<=10:

In[2]:=

ParametricPlot[F[t], {t, -10, 10}]

[Graphics:HTMLFiles/index_3.gif]

Out[2]=

⁃Graphics⁃

Is this really a circle???
Add the option "AspectRatio→Automatic" to make the x and y coordinates appear in the same scale:

In[3]:=

ParametricPlot[F[t], {t, -10, 10}, AspectRatioAutomatic]

[Graphics:HTMLFiles/index_6.gif]

Out[3]=

⁃Graphics⁃

Created by Mathematica  (September 13, 2004)