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Chapter 9: Q. 45 (page 772)

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

r=21-3cos胃

Short Answer

Expert verified

The graph will be

Step by step solution

01

Step 1. Given information.

The given equation isr=21-3cos胃.

02

Step 2. Comparison.

On comparing the given equation with standard form,

r=eu1+ecos胃The eccentricitye=-3Hereeu=2-3路u=2鈬�u=-23

03

Step 3. Graph.

For r=21-3cos胃the eccentricity ise=-3,so the graph is a hyperbola. The directrix will be the vertical linex=-23

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Most popular questions from this chapter

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.

-2,0

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.

r=胃

Explain why there are infinitely many different ellipses with the same foci.

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

r=31+cos胃

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.

foci0,卤332, minor axis3
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