Chapter 11: Q. 47 (page 1083)

In the following exercises, (a) identify the center and radius and (b) graph.
$x^{2} + y^{2} + 4 x = 0$

Short Answer

Expert verified

(a) The center and radius of the graph $x^{2} + y^{2} + 4 x = 0$ is $(- 2, 0)$ and $r = 2$

(b) The graph of the function is:

Step by step solution

Part (a) Step 1. Given

The function $x^{2} + y^{2} + 4 x = 0$

To find the radius and center of the circle.

Part (a) Step 2. Group terms x,y-

Group the $x -$ terms and $y -$ terms. Collect the constants on the right side.

$x^{2} + y^{2} + 4 x = 0 x^{2} + 4 x + y^{2} = 0 x^{2} + 4 x + 4 + y^{2} - 4 = 0$

Part (a) Step 3. Complete the squares.

Complete the squares and write in binomial form.

$x^{2} + 4 x + 4 - 4 + y^{2} = 0 {(x + 2)}^{2} + y^{2} = 4$

Part (a) Step 4. Identify the center and radius.

Identify the center and radius by comparing the equation with standard form of circle ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ .

From the equation, the center is $(- 2, 0)$ and the radius is $2$

Part (b) Step 1. Given

The function $x^{2} + y^{2} + 4 x = 0$

To graph the function

Part (b) Step 2. Graph the function

Graph the circle with center $(- 2, 0)$ and radius $2$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, (a) identify the center and radius and (b) graph.
$x^{2} + y^{2} + 4 x = 0$

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Group terms x,y-

Part (a) Step 3. Complete the squares.

Part (a) Step 4. Identify the center and radius.

Part (b) Step 1. Given

Part (b) Step 2. Graph the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, (a) identify the center and radius and (b) graph.x2+y2+4x=0

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Group terms x,y-

Part (a) Step 3. Complete the squares.

Part (a) Step 4. Identify the center and radius.

Part (b) Step 1. Given

Part (b) Step 2. Graph the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, (a) identify the center and radius and (b) graph.
$x^{2} + y^{2} + 4 x = 0$