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. $$x=\cos (2 t), \quad y=\sin t$$

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. $$x=4 t+3, y=16 t^{2}-9$$

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. $$x=t^{n}, \quad y=n \ln t, t \geq 1$$ 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. $$\begin{array}{l}{x-4=5 t} \\ {y+2=t}\end{array}$$