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Q. 51

Found in: Page 772


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Use polar coordinates to graph the conics in Exercises 44–51.


The graph is

See the step by step solution

Step by Step Solution

Step 1. Given information.

The given equation is r=22+sinθ.

Step 2. Comparison.

On comparing the given equation with standard form r=eu1+esinθ.

r=222+sinθ2r=11+12sinθ Here eu=1 The eccentricity e=12u=2

Step 3. Graph.

For r=22+sinθthe eccentricity is e=12, so the graph is an ellipse. The directrix is parallel to the polar axis at a distance u=2 units above the pole. The directrix is 2 units above the pole .

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