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Chapter 9: Q. 49 (page 772)

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

r=24+sin胃

Short Answer

Expert verified

The graph is

Step by step solution

01

Step 1. Given information.

The given equation isr=24+sin胃.

02

Step 2. Comparison.

On comparing the given equation with standard equationr=eu1+esin胃,

r=24+sin胃r=244+sin胃4r=1244+sin胃4r=121+14sin胃The eccentricitye=14Here eu=12u=2

03

Step 3. Graph.

For r=24+sin胃the eccentricity is e=14, so the graph is an ellipse. The directrix is parallel to the polar axis at a distance u=2units above the pole. That means the directrix is u=2units above the pole.

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Most popular questions from this chapter

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

r=51+cos胃

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

r=22+sin胃

Each of the integrals or integral expressions in Exercises 38-44represents the area of a region in the plane. Use polar coordinates to sketch the region and evaluate the expressions.

role="math" localid="1649518287481" 3鈭�0蟺/2sin23胃d胃.

Complete the square to describe the conics in Exercises 18-21.

role="math" localid="1649636875685" 4x+y2-6y-3=0

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

r=sin3胃
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