The equation of a circle is (x + 10)² + (y − 4)² = 100. - What is the center and radius of the circle? 4); radius: 10 center: (-10, 4); radius: 10,000 O center: (10,- 4); radius: 10,000 O center: (-10, 4); radius: O center: (10, -
The equation of a circle is (x + 10)² + (y − 4)² = 100. - What is the center and radius of the circle? 4); radius: 10 center: (-10, 4); radius: 10,000 O center: (10,- 4); radius: 10,000 O center: (-10, 4); radius: O center: (10, -
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
![**Understanding the Equation of a Circle**
The equation of a circle given is:
\[
(x + 10)^2 + (y - 4)^2 = 100
\]
### Determining the Center and Radius:
To find the center and radius of the circle, compare the given equation with the standard form of the circle equation:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) represents the center of the circle, and \(r\) represents the radius.
### Given Equation:
\[
(x + 10)^2 + (y - 4)^2 = 100
\]
From the equation, we can see:
- \(h = -10\) (since \(x + 10 = x - (-10)\))
- \(k = 4\)
So, the center of the circle is \((-10, 4)\).
To find the radius \(r\), recognize that \(100\) is \(r^2\):
\[
r^2 = 100 \implies r = \sqrt{100} = 10
\]
Therefore, the radius \(r\) is \(10\).
### Answer Choices:
- center: \((10, -4)\); radius: \(10\)
- center: \((-10, 4)\); radius: \(10,000\)
- center: \((10, -4)\); radius: \(10,000\)
- center: \((-10, 4)\); radius: \(10\)
### Correct Answer:
The correct option is:
- **center: \((-10, 4)\); radius: \(10\)**
By understanding the form and comparing given values, we have determined the center and radius of the circle accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b717370-ac2a-4449-94d5-6954bef42bac%2F48f0f89f-6c91-44a7-95e8-5b87ce190dcf%2Fdcfhh2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Equation of a Circle**
The equation of a circle given is:
\[
(x + 10)^2 + (y - 4)^2 = 100
\]
### Determining the Center and Radius:
To find the center and radius of the circle, compare the given equation with the standard form of the circle equation:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) represents the center of the circle, and \(r\) represents the radius.
### Given Equation:
\[
(x + 10)^2 + (y - 4)^2 = 100
\]
From the equation, we can see:
- \(h = -10\) (since \(x + 10 = x - (-10)\))
- \(k = 4\)
So, the center of the circle is \((-10, 4)\).
To find the radius \(r\), recognize that \(100\) is \(r^2\):
\[
r^2 = 100 \implies r = \sqrt{100} = 10
\]
Therefore, the radius \(r\) is \(10\).
### Answer Choices:
- center: \((10, -4)\); radius: \(10\)
- center: \((-10, 4)\); radius: \(10,000\)
- center: \((10, -4)\); radius: \(10,000\)
- center: \((-10, 4)\); radius: \(10\)
### Correct Answer:
The correct option is:
- **center: \((-10, 4)\); radius: \(10\)**
By understanding the form and comparing given values, we have determined the center and radius of the circle accurately.
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