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Chapter 9: Q 36. (page 731)

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.
$r = 2 \cos 胃$

Short Answer

Expert verified

The required equation is ${(x - 1)}^{2} + y^{2} = 1$ .

Step by step solution

01

Step 1. Given information.

The given equation in polar coordinates is:

$r = 2 \cos 胃$

02

Step 2. Find the equation in rectangular coordinates.

$r = 2 \cos 胃$

First, multiply both sides byr,

$r^{2} = 2 r \cos 胃 r^{2} = 2 x [Since r \cos 胃 = x] x^{2} + y^{2} = 2 x [S i n c e r^{2} = x^{2} + y^{2}]$

Now add $- 2 x$ on both sides of the equation,

role="math" localid="1649264450788" $x^{2} + y^{2} - 2 x = 2 x - 2 x x^{2} + y^{2} - 2 x = 0$

Complete the square in x,

${(x - 1)}^{2} + y^{2} - 1 = 0$

now add 1 on both sides of the equation,

${(x - 1)}^{2} + y^{2} - 1 + 1 = 0 + 1 {(x - 1)}^{2} + y^{2} = 1$

Therefore, the equation in rectangular coordinates is ${(x - 1)}^{2} + y^{2} = 1$ .

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Most popular questions from this chapter

Each of the integral in exercise 38-44 represents the area of a region in a plane use polar coordinates to sketch the region and evaluate the expression

The integral is $A = {鈭�}_{- \frac{蟺}{2}}^{\frac{蟺}{2}} {(2 - \sin 胃)}^{2} d 胃$

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

role="math" localid="1649636875685" $4 x + y^{2} - 6 y - 3 = 0$

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

$r = 胃$

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.
$胃 = \frac{7 蟺}{6}$

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

$(0, - 3)$

See all solutions

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