91Ó°ÊÓ

Use a graphing utility to graph the following curves. Be sure to choose an interval for the parameter that generates all features of interest. $$\text { Folium of Descartes } x=\frac{3 t}{1+t^{3}}, y=\frac{3 t^{2}}{1+t^{3}}$$

Find the area of the following regions. The region inside the limaçon \(r=4-2 \cos \theta\)

Find the area of the following regions. The region inside the complete three-leaf rose \(r=2 \cos 3 \theta\)

Use a graphing utility to graph the following curves. Be sure to choose an interval for the parameter that generates all features of interest. $$\text { Involute of a circle } x=\cos t+t \sin t, y=\sin t-t \cos t$$

Graph the following conic sections, labeling the vertices, foci, directrices, and asymptotes (if they exist ). Use a graphing utility to check your work. $$r=\frac{6}{3+2 \sin \theta}$$

Graph the following equations. Use a graphing utility to check your work and produce a final graph. $$r^{2}=4 \sin \theta$$

Graph the following equations. Use a graphing utility to check your work and produce a final graph. $$r^{2}=16 \cos \theta$$

Use a graphing utility to graph the following curves. Be sure to choose an interval for the parameter that generates all features of interest. Evolute of an ellipse \(x=\frac{a^{2}-b^{2}}{a} \cos ^{3} t, y=\frac{a^{2}-b^{2}}{b} \sin ^{3} t\) ; \(a=4\) and \(b=3\)

Graph the following equations. Use a graphing utility to check your work and produce a final graph. $$r^{2}=16 \sin 2 \theta$$

Graph the following conic sections, labeling the vertices, foci, directrices, and asymptotes (if they exist ). Use a graphing utility to check your work. $$r=\frac{12}{3-\cos \theta}$$