First, we note that the parameter in this problem is r instead of t .This makes absolutely no difference since, as in the case of the variable of integration, the parameter is a “dummy” variable. Now to get a feeling for the shape of this curve, we display in Table 1, values of x and y for various values of r .Plotting some of these points leads to the sketch in Figure 3. To write the Cartesian equation for this curve we square both sides of the equation y=r^{2} to obtain y^{2}=r^{4} and x=1-r^{4}=1-y^{2} which is the equation of the parabola sketched in Figure 4. Note that this curve is not the same as the curve sketched in Figure 3 since the parametric representation y=r^{2} requires that y be nonnegative. Thus the curve described by (6)

is only the upper half of the parabola described by the equation x=1-y^{2}.