91Ó°ÊÓ

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$ x=t^{2}, \quad y=2 \ln t, t \geq 1 $$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$ x=t^{3}, \quad y=3 \ln t, t \geq 1 $$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. \(x=t^{n}, \quad y=n \ln t, t \geq 1, \quad\) where \(n\) is a natural number

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$ \begin{array}{l} x=\ln (5 t) \\ y=\ln \left(t^{2}\right) \text { where } 1 \leq t \leq e \end{array} $$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$ \begin{array}{l} x=2 \sin (8 t) \\ y=2 \cos (8 t) \end{array} $$

For the following exercises, convert the parametric equations of a curve into rectangular form. No sketch is necessary. State the domain of the rectangular form. $$ \begin{array}{l} x=\tan t \\ y=\sec ^{2} t-1 \end{array} $$

For the following exercises, the pairs of parametric equations represent lines, parabolas, circles, ellipses, or hyperbolas. Name the type of basic curve that each pair of equations represents. $$ \begin{array}{l} x=3 t+4 \\ y=5 t-2 \end{array} $$

For the following exercises, the pairs of parametric equations represent lines, parabolas, circles, ellipses, or hyperbolas. Name the type of basic curve that each pair of equations represents. $$ \begin{array}{l} x-4=5 t \\ y+2=t \end{array} $$

For the following exercises, the pairs of parametric equations represent lines, parabolas, circles, ellipses, or hyperbolas. Name the type of basic curve that each pair of equations represents. $$ \begin{array}{l} x=2 t+1 \\ y=t^{2}-3 \end{array} $$

For the following exercises, the pairs of parametric equations represent lines, parabolas, circles, ellipses, or hyperbolas. Name the type of basic curve that each pair of equations represents. $$ \begin{array}{l} x=2 t+1 \\ y=t^{2}-3 \end{array} $$