91Ó°ÊÓ

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. $$\begin{array}{l}{x=3 \cos t} \\ {y=3 \sin t}\end{array}$$

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. $$\begin{array}{l}{x=2 \cos (3 t)} \\ {y=2 \sin (3 t)}\end{array}$$

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. $$\begin{array}{l}{x=\cosh t} \\ {y=\sinh t}\end{array}$$

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. $$\begin{array}{l}{x=3 \cos t} \\ {y=4 \sin t}\end{array}$$

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. $$\begin{array}{l}{x=2 \cos (3 t)} \\ {y=5 \sin (3 t)}\end{array}$$

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. $$\begin{array}{l}{x=3 \cosh (4 t)} \\ {y=4 \sinh (4 t)}\end{array}$$

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. $$\begin{array}{l}{x=2 \cosh t} \\ {y=2 \sinh t}\end{array}$$

Show that $$\begin{array}{l}{x=h+r \cos \theta} \\ {y=k+r \sin \theta}\end{array}$$ represents the equation of a circle.

For the following exercises, use a graphing utility to graph the curve represented by the parametric equations and identify the curve from its equation. $$\begin{array}{l}{x=\theta+\sin \theta} \\ {y=1-\cos \theta}\end{array}$$