91Ó°ÊÓ

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. \(x=t^{2}+t, \quad y=t^{2}-t\)

Find the area of the region.One petal of \(r=6 \sin 2 \theta\)

Find \(d y / d x\) and \(d^{2} y / d x^{2}\), and find the slope and concavity (if possible) at the given value of the parameter. $$ \begin{array}{ll} \underline{\text { Parametric Equations }} & \underline{\text { Point }} \\ x=2 \cos \theta, y=2 \sin \theta &\quad \theta=\frac{\pi}{4} \end{array} $$

Find the vertex, focus, and directrix of the parabola, and sketch its graph. $$ y^{2}=-6 x $$

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. \(x=\sqrt{t}, \quad y=t-2\)

Find the area of the region.One petal of \(r=\cos 2 \theta\)

Use the angle feature of a graphing utility to find the rectangular coordinates for the point given in polar coordinates. Plot the point. $$ (8.25,1.3) $$

Find the area of the region.One petal of \(r=\cos 5 \theta\)

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. \(x=\sqrt[4]{t}, \quad y=3-t\)

Find \(d y / d x\) and \(d^{2} y / d x^{2}\), and find the slope and concavity (if possible) at the given value of the parameter. $$ \begin{array}{ll} \underline{\text { Parametric Equations }} & \underline{\text { Point }} \\ x=\cos \theta, y=3 \sin \theta &\quad \theta=0 \end{array} $$