91Ó°ÊÓ

Find a polar equation that has the same graph as the equation in \(x\) and \(y.\) $$ y^{2}-x^{2}=4 $$

Set up an integral in polar coordinates that can be used to find the area of the region bounded by the graphs of the equations. \(r=2 \sec \theta ; \quad \theta=\pi / 6, \quad \theta=\pi / 3\)

Find an equation in \(x\) and \(y\) that has the same graph as the polar equation. $$ r^{2}=\tan \theta $$

Find a polar equation that has the same graph as the equation in \(x\) and \(y.\) $$ x y=8 $$

Exer. 29-34: Find the area of the surface generated by revolving the curve about the \(x\) -axis. $$ \begin{array}{ll} x=t, & y=\frac{1}{3} t^{3}+\frac{1}{4} t^{-1} ; \quad 1 \leq t \leq 2 \end{array} $$

Set up an integral in polar coordinates that can be used to find the area of the region bounded by the graphs of the equations. \(r=\csc \theta \cot \theta ; \quad \theta=\pi / 6, \quad \theta=\pi / 4\)

Find an equation in \(x\) and \(y\) that has the same graph as the polar equation. $$ r=2 \cos \theta+3 \sin \theta $$

Exer. \(35-38:\) Find the area of the surface generated by revolving the graph of the equation about the polar axis. \(r^{2}=4 \cos 2 \theta\)

Find an equation in \(x\) and \(y\) that has the same graph as the polar equation. $$ r^{2}=4 \sin 2 \theta $$

Find a polar equation that has the same graph as the equation in \(x\) and \(y.\) \(x^{3}+y^{3}-3 a x y=0\) (Folium of Descartes)