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
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Answer question 9
![**9. What is an equation of the circle with center (5, 13) and a radius of 9 units?**
To find the equation of a circle with a given center and radius, we use the standard form of the equation of a circle:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
In this problem, the center \((h, k)\) is given as \((5, 13)\) and the radius \(r\) is given as 9 units. Substituting these values into the standard form equation:
\[
(x - 5)^2 + (y - 13)^2 = 9^2
\]
Simplifying further:
\[
(x - 5)^2 + (y - 13)^2 = 81
\]
So, the equation of the circle is:
\[
(x - 5)^2 + (y - 13)^2 = 81
\]
This equation represents a circle with a center at the point \((5, 13)\) and a radius of 9 units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48b0c420-ba29-475d-827a-2f33ce024949%2F5f80da9d-90a9-46e6-9f73-b741f8600905%2Fmnf7eq3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**9. What is an equation of the circle with center (5, 13) and a radius of 9 units?**
To find the equation of a circle with a given center and radius, we use the standard form of the equation of a circle:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
In this problem, the center \((h, k)\) is given as \((5, 13)\) and the radius \(r\) is given as 9 units. Substituting these values into the standard form equation:
\[
(x - 5)^2 + (y - 13)^2 = 9^2
\]
Simplifying further:
\[
(x - 5)^2 + (y - 13)^2 = 81
\]
So, the equation of the circle is:
\[
(x - 5)^2 + (y - 13)^2 = 81
\]
This equation represents a circle with a center at the point \((5, 13)\) and a radius of 9 units.
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