Chapter 8: Problem 18
In Exercises \(17-20,\) use a graphing utility to graph the polar equation. Identify the graph. \(r=\frac{-3}{2+4 \sin \theta}\)
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Give the integral formulas for area and arc length in polar coordinates.
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. $$ x=4 \sin 2 \theta, y=2 \cos 2 \theta $$
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $$ x=1+\frac{1}{t}, \quad y=t-1 $$
Use the results of Exercises \(31-34\) to find a set of parametric equations for the line or conic. $$ \text { Ellipse: vertices: }(\pm 5,0) ; \text { foci: }(\pm 4,0) $$
What conic section does \(r=a \sin \theta+b \cos \theta\) represent? \(?\)
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