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:

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

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

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

F[t]

F[0]

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

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

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

ParametricPlot[F[t], {t, 5, 100}, AspectRatio -> Automatic]