H O The center of a circle is at (-3, 1) and its radius is 9. What is the equation of the circle? O (x+3)² + (y-1)² = 81 O(x-3)² + (y + 1)² = 81 O (x+3)² + (y-1)² = 18 O(x-3)² + (y + 1)² = 18 3 4 $ 4 ER 5 T 6 & 7 1
H O The center of a circle is at (-3, 1) and its radius is 9. What is the equation of the circle? O (x+3)² + (y-1)² = 81 O(x-3)² + (y + 1)² = 81 O (x+3)² + (y-1)² = 18 O(x-3)² + (y + 1)² = 18 3 4 $ 4 ER 5 T 6 & 7 1
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
![### Circle Equation Determination
#### Problem Statement:
The center of a circle is at \((-3, 1)\) and its radius is 9.
**Question:**
What is the equation of the circle?
#### Options:
- \((x + 3)^2 + (y - 1)^2 = 81\)
- \((x - 3)^2 + (y + 1)^2 = 81\)
- \((x + 3)^2 + (y - 1)^2 = 18\)
- \((x - 3)^2 + (y + 1)^2 = 18\)
### Explanation:
In this problem, you are given the center \((h, k)\) of the circle and its radius \(r\). The standard form of the equation of a circle is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Substituting \(h = -3\), \(k = 1\), and \(r = 9\):
\[
(x - (-3))^2 + (y - 1)^2 = 9^2
\]
\[
(x + 3)^2 + (y - 1)^2 = 81
\]
Therefore, the correct answer is:
- \((x + 3)^2 + (y - 1)^2 = 81\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b717370-ac2a-4449-94d5-6954bef42bac%2Ff114ecc3-60cf-4c30-926f-6a3298f9083b%2Fvdb7t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Circle Equation Determination
#### Problem Statement:
The center of a circle is at \((-3, 1)\) and its radius is 9.
**Question:**
What is the equation of the circle?
#### Options:
- \((x + 3)^2 + (y - 1)^2 = 81\)
- \((x - 3)^2 + (y + 1)^2 = 81\)
- \((x + 3)^2 + (y - 1)^2 = 18\)
- \((x - 3)^2 + (y + 1)^2 = 18\)
### Explanation:
In this problem, you are given the center \((h, k)\) of the circle and its radius \(r\). The standard form of the equation of a circle is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Substituting \(h = -3\), \(k = 1\), and \(r = 9\):
\[
(x - (-3))^2 + (y - 1)^2 = 9^2
\]
\[
(x + 3)^2 + (y - 1)^2 = 81
\]
Therefore, the correct answer is:
- \((x + 3)^2 + (y - 1)^2 = 81\)
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