Write the standard form of the equation of the circle with its center at (-6,0), and a radius of 4. What is the equation of the circle in standard form?
Write the standard form of the equation of the circle with its center at (-6,0), and a radius of 4. What is the equation of the circle in standard form?
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Equation of a Circle in Standard Form
#### Problem Statement:
Write the standard form of the equation of the circle with its center at \((-6, 0)\), and a radius of 4.
What is the equation of the circle in standard form?
#### Solution:
The standard form of the equation of a circle is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Where:
- \((h, k)\) is the center of the circle
- \(r\) is the radius of the circle
Given:
- The center of the circle \((h, k)\) is \((-6, 0)\)
- The radius \(r\) is 4
Substitute these values into the standard form equation:
\[
(x - (-6))^2 + (y - 0)^2 = 4^2
\]
Simplify the equation:
\[
(x + 6)^2 + y^2 = 16
\]
Thus, the equation of the circle in standard form is:
\[
(x + 6)^2 + y^2 = 16
\]
##### Interactive Component:
Enter your answer in the answer box and then click "Check Answer."
[Check Answer button]
---
#### Note:
There are no graphs or diagrams accompanying the given text. If a visual representation of the circle is needed, a plot can be created showing a circle centered at \((-6, 0)\) with a radius of 4 on the xy-plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04d98a3f-fb1a-4d25-a40d-dbae4efec7f3%2Fd06f0f08-52da-486d-9658-14e0b4f6aede%2Fh1xhls_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Equation of a Circle in Standard Form
#### Problem Statement:
Write the standard form of the equation of the circle with its center at \((-6, 0)\), and a radius of 4.
What is the equation of the circle in standard form?
#### Solution:
The standard form of the equation of a circle is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Where:
- \((h, k)\) is the center of the circle
- \(r\) is the radius of the circle
Given:
- The center of the circle \((h, k)\) is \((-6, 0)\)
- The radius \(r\) is 4
Substitute these values into the standard form equation:
\[
(x - (-6))^2 + (y - 0)^2 = 4^2
\]
Simplify the equation:
\[
(x + 6)^2 + y^2 = 16
\]
Thus, the equation of the circle in standard form is:
\[
(x + 6)^2 + y^2 = 16
\]
##### Interactive Component:
Enter your answer in the answer box and then click "Check Answer."
[Check Answer button]
---
#### Note:
There are no graphs or diagrams accompanying the given text. If a visual representation of the circle is needed, a plot can be created showing a circle centered at \((-6, 0)\) with a radius of 4 on the xy-plane.
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