91Ó°ÊÓ

In exercises find the area enclosed by the given curve. $$\left\\{\begin{array}{l} x=2 \cos 2 t+\cos 4 t \\ y=2 \sin 2 t+\sin 4 t \end{array}\right.$$

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis. $$\left\\{\begin{array}{l} x=t^{2}-1 \\ y=t^{3}-4 t \end{array},-2 \leq t \leq 0, \text { about } x=-1\right.$$

Find parametric equations of the conic sections. $$\frac{(x-2)^{2}}{9}-\frac{(y+1)^{2}}{16}=1$$

Describe the role that \(r\) plays in the graph of $$\begin{aligned} &\left\\{\begin{array}{l}x=r \cos t \\\y=r \sin t\end{array}\text { and then describe how to sketch the graph of }\right.\\\&\left\\{\begin{array}{l}x=t \cos t \\\y=t \sin t\end{array}\right.\end{aligned}$$

Graph the conic section and find an equation. All points equidistant from the point (2,1) and the line \(y=-3\)

Compute the surface area of the surface obtained by revolving the given curve about the indicated axis. $$\left\\{\begin{array}{l} x=t^{3}-4 t \\ y=t^{2}-3 \end{array}, 0 \leq t \leq 2, \text { about the } y\text { -axis }\right.$$

Find the area of the indicated region. Inside of \(r=3+2 \sin \theta\) and outside of \(r=2\)

Sketch the graph of the polar equation and find a corresponding \(x-y\) equation. $$r=3 \sin \theta$$

In exercises find the area enclosed by the given curve. $$\left\\{\begin{array}{l} x=\cos t \\ y=\sin 2 t \end{array}, \frac{\pi}{2} \leq t \leq \frac{3 \pi}{2}\right.$$

Find parametric equations of the conic sections. $$\frac{(x+1)^{2}}{16}-\frac{y^{2}}{9}=1$$