10.6E: Parametric Equations (Exercises)
For the following exercises, eliminate the parameter \(t\) to rewrite the parametric equation as a Cartesian equation.
44. \(\left\{\begin{array}{l}x(t)=3 t-1 \\ y(t)=\sqrt{t}\end{array}\right.\)
45. \(\left\{\begin{array}{l}x(t)=-\cos t \\ y(t)=2 \sin ^{2} t\end{array}\right.\)
46. Parameterize (write a parametric equation for) each Cartesian equation by using \(x(t)=a \cos t\) and \(y(t)=\mathbf{b} \sin t\) for \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\)
47. Parameterize the line from (-2,3) to (4,7) so that the line is at (-2,3) at \(t=0\) and (4,7) at \(t=1\).