91Ó°ÊÓ

Find the points of intersection of the graphs of the equations. $$ \begin{array}{l} r=1+\cos \theta \\ r=3 \cos \theta \end{array} $$

Use the angle feature of a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. $$ (3 \sqrt{2}, 3 \sqrt{2}) $$

In Exercises \(7-16,\) find the eccentricity and the distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. \(r=\frac{4}{1+2 \cos \theta}\)

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$ x=2 \cos \theta, \quad y=6 \sin \theta $$

In Exercises \(17-20,\) use a graphing utility to graph the polar equation. Identify the graph. \(r=\frac{3}{-4+2 \sin \theta}\)

Find the points of intersection of the graphs of the equations. $$ \begin{array}{l} r=\frac{\theta}{2} \\ r=2 \end{array} $$

Use the angle feature of a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. $$ \left(\frac{5}{2}, \frac{4}{3}\right) $$

Use a graphing utility to graph the curve represented by the parametric equations (indicate the orientation of the curve). Eliminate the parameter and write the corresponding rectangular equation. $$ x=4 \sin 2 \theta, y=2 \cos 2 \theta $$

Use a graphing utility to graph the curve represented by the parametric equations (indicate the orientation of the curve). Eliminate the parameter and write the corresponding rectangular equation. $$ x=\cos \theta, y=2 \sin 2 \theta $$

In Exercises \(17-20,\) use a graphing utility to graph the polar equation. Identify the graph. \(r=\frac{-3}{2+4 \sin \theta}\)