91Ó°ÊÓ

Sketch the strophoid \(r=\sec \theta-2 \cos \theta\) \(-\frac{\pi}{2}<\theta<\frac{\pi}{2}\). Convert this equation to rectangular coordinates. Find the area enclosed by the loop.

Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. $$ x=\sec \theta, \quad y=\tan \theta $$

Convert the polar equation to rectangular form and sketch its graph. $$ r=3 \sec \theta $$

Eliminate the parameter and obtain the standard form of the rectangular equation. $$ \text { Ellipse: } x=h+a \cos \theta, \quad y=k+b \sin \theta $$

In Exercises 33-36, find the length of the curve over the given interval. $$ \begin{array}{ll} \text { Polar Equation } & \text { Interval } \\ \hline r=a & 0 \leq \theta \leq 2 \pi \end{array} $$

Eliminate the parameter and obtain the standard form of the rectangular equation. $$ \text { Hyperbola: } x=h+a \sec \theta, \quad y=k+b \tan \theta $$

Convert the polar equation to rectangular form and sketch its graph. $$ r=2 \csc \theta $$

Find the length of the curve over the given interval. $$ \begin{array}{ll} \text { Polar Equation } & \text { Interval } \\ \hline r=2 a \cos \theta & -\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2} \end{array} $$

Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. $$ x=\cos ^{2} \theta, \quad y=\cos \theta $$

Use a graphing utility to graph the polar equation. Find an interval for \(\boldsymbol{\theta}\) over which the graph is traced only once. $$ r=3-4 \cos \theta $$