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Chapter 9: Q 43. (page 731)

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

r2=cos胃

Short Answer

Expert verified

The required equation isx2+y232=x.

Step by step solution

01

Step 1. Given information.

The given equation in polar coordinates is:

r2=cos胃

02

Step 2. Find the equation in rectangular coordinates.

r2=cos胃
First, multiply both sides byr,

r路r2=rcos胃r3=xSincex=rcos胃x2+y23=xr2=x2+y2andr=x2+y2x2+y232=x

Therefore, the equation in rectangular coordinates isx2+y232=x.

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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.

6,23

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

胃=蟺

Complete the square to describe the conics in Exercises 18鈥�21 .

y2-8y-4x2-8x-13=0

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.

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

r=21+3cos胃
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