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Chapter 11: Problem 4
What is the polar equation of a circle of radius \(|a|\) centered at the origin?
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Sketch the graph of the following parabolas. Specify the location of the focus and the equation of the directrix. Use a graphing utility to check your work. $$4 x=-y^{2}$$
Let \(R\) be the region bounded by the upper half of the ellipse \(x^{2} / 2+y^{2}=1\) and the parabola \(y=x^{2} / \sqrt{2}\) a. Find the area of \(R\). b. Which is greater, the volume of the solid generated when \(R\) is revolved about the \(x\) -axis or the volume of the solid generated when \(R\) is revolved about the \(y\) -axis?
Graph the following conic sections, labeling the vertices, foci, directrices, and asymptotes (if they exist). Use a graphing utility to check your work. $$r=\frac{6}{3+2 \sin \theta}$$
Find an equation of the following curves, assuming the center is at the origin. Sketch a graph labeling the vertices, foci, asymptotes, and directrices. Use a graphing utility to check your work. An ellipse with vertices (0,卤9) and eccentricity \(\frac{1}{4}\)
Consider an ellipse to be the set of points in a plane whose distances from two fixed points have a constant sum 2 \(a .\) Derive the equation of an ellipse. Assume the two fixed points are on the \(x\) -axis equidistant from the origin.
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