Chapter 9: Q. 49 (page 772)

Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{4 + \sin θ}$

Short Answer

Expert verified

The graph is

Step by step solution

Step 1. Given information.

The given equation is $r = \frac{2}{4 + \sin θ} .$

Step 2. Comparison.

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

$r = \frac{2}{4 + \sin θ} r = \frac{\frac{2}{4}}{\frac{4 + \sin θ}{4}} r = \frac{\frac{1}{2}}{\frac{4}{4} + \frac{\sin θ}{4}} r = \frac{\frac{1}{2}}{1 + \frac{1}{4} \sin θ} The eccentricity e = \frac{1}{4} Here eu = \frac{1}{2} u = 2$

Step 3. Graph.

For $r = \frac{2}{4 + \sin θ}$ the eccentricity is $e = \frac{1}{4}$ , so the graph is an ellipse. The directrix is parallel to the polar axis at a distance $u = 2$ units above the pole. That means the directrix is $u = 2$ units above the pole.

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Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{4 + \sin θ}$

Short Answer

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=24+sinθ

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Comparison.

Step 3. Graph.

One App. One Place for Learning.

Most popular questions from this chapter

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Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{4 + \sin θ}$