91Ó°ÊÓ

In exercises parametric equations for the position of an object are given. Find the object's velocity and speed at the given times and describe its motion. $$ \left\\{\begin{array}{l} x=\cos 2 t \\ y=\sin \pi t \end{array}\right. $$

Find rectangular coordinates for the given polar point. $$\left(3, \frac{\pi}{8}\right)$$

Identify the conic section and find each vertex, focus and directrix. $$\frac{(x+2)^{2}}{16}+\frac{y^{2}}{4}=1$$

In exercises parametric equations for the position of an object are given. Find the object's velocity and speed at the given times and describe its motion $$\left\\{\begin{array}{l} x=2 \cos 2 t \\ y=2 \sin 2 t \end{array}\right.$$

Find rectangular coordinates for the given polar point. $$\left(4, \frac{\pi}{10}\right)$$

Use your CAS or graphing calculator to sketch the plane curves defined by the given parametric equations. $$\left\\{\begin{array}{l}x=3 \cos 2 t+\sin 5 t \\\y=3 \sin 2 t+\cos 5 t\end{array}\right.$$

Identify the conic section and find each vertex, focus and directrix. $$\frac{(x-1)^{2}}{9}-\frac{y^{2}}{4}=1$$

Graph and interpret the conic section. $$r=\frac{4}{2 \cos (\theta-\pi / 6)+1}$$

Use your CAS or graphing calculator to sketch the plane curves defined by the given parametric equations. $$\left\\{\begin{array}{l}x=3 \cos 2 t+\sin 6 t \\\y=3 \sin 2 t+\cos 6 t\end{array}\right.$$

Identify the conic section and find each vertex, focus and directrix. $$\frac{(x+1)^{2}}{4}-\frac{(y-3)^{2}}{4}=1$$