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 standard form of the equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\), where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius of the circle.
### Example Problem
Consider the following equation of a circle:
\[
(x - 10)^2 + (y - 8)^2 = 256
\]
**Question:** What is the center of the circle?
**Solution:**
To determine the center of the circle, we compare the given equation with the standard form \((x - h)^2 + (y - k)^2 = r^2\).
From the given equation:
- \(h = 10\)
- \(k = 8\)
Therefore, the center of the circle is \((10, 8)\).
**Answer:**
Enter your answer in the boxes provided:
[10] [8]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b717370-ac2a-4449-94d5-6954bef42bac%2Fb6e8fbc5-744a-4be2-b831-723fd2bc69fc%2Fkseuv2c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Equation of a Circle**
The standard form of the equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\), where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius of the circle.
### Example Problem
Consider the following equation of a circle:
\[
(x - 10)^2 + (y - 8)^2 = 256
\]
**Question:** What is the center of the circle?
**Solution:**
To determine the center of the circle, we compare the given equation with the standard form \((x - h)^2 + (y - k)^2 = r^2\).
From the given equation:
- \(h = 10\)
- \(k = 8\)
Therefore, the center of the circle is \((10, 8)\).
**Answer:**
Enter your answer in the boxes provided:
[10] [8]
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