Short Answer

Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{2 + \sin θ}$

The graph is

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given equation is $r = \frac{2}{2 + \sin θ}$ .

Step 2. Comparison.

On comparing the given equation with standard form $r = \frac{e u}{1 + e \sin θ}$ .

$r = \frac{\frac{2}{2}}{\frac{2 + \sin θ}{2}} r = \frac{1}{1 + \frac{1}{2} \sin θ} Here e u = 1 The eccentricity e = \frac{1}{2} u = 2$

Step 3. Graph.

For $r = \frac{2}{2 + \sin θ}$ the eccentricity is $e = \frac{1}{2}$ , 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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Short Answer

Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{2 + \sin θ}$

Step by Step Solution

Step 1. Given information.

Step 2. Comparison.

Step 3. Graph.

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Step by Step Solution

Step 1. Given information.

Step 2. Comparison.

Step 3. Graph.

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Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{2 + \sin θ}$