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
To determine the equation of a circle, we use the standard form of the equation:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \( (h, k) \) is the center of the circle and \( r \) is the radius.
From the graph:
- The center of the circle is at \( (4, 4) \).
- The radius of the circle is 3 units (determined by the distance from the center to any point on the circle).
Using these values, we substitute \( h = 4 \), \( k = 4 \), and \( r = 3 \) into the standard form equation:
\[ (x - 4)^2 + (y - 4)^2 = 3^2 \]
\[ (x - 4)^2 + (y - 4)^2 = 9 \]
Therefore, the equation of the circle is:
\[ (x - 4)^2 + (y - 4)^2 = 9 \]
In the graph provided, the circle is centered at point (4, 4) and extends 3 units outwards in all directions, forming a perfect circle around the center.
If you have any further questions or need additional help with graphing equations, please refer to our library of educational materials or consult the instructional videos available on our platform.
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Transcribed Image Text:---
**Determine the equation of the circle graphed below.**
To determine the equation of a circle, we use the standard form of the equation:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \( (h, k) \) is the center of the circle and \( r \) is the radius.
From the graph:
- The center of the circle is at \( (4, 4) \).
- The radius of the circle is 3 units (determined by the distance from the center to any point on the circle).
Using these values, we substitute \( h = 4 \), \( k = 4 \), and \( r = 3 \) into the standard form equation:
\[ (x - 4)^2 + (y - 4)^2 = 3^2 \]
\[ (x - 4)^2 + (y - 4)^2 = 9 \]
Therefore, the equation of the circle is:
\[ (x - 4)^2 + (y - 4)^2 = 9 \]
In the graph provided, the circle is centered at point (4, 4) and extends 3 units outwards in all directions, forming a perfect circle around the center.
If you have any further questions or need additional help with graphing equations, please refer to our library of educational materials or consult the instructional videos available on our platform.
---
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