Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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#### Graph Details:
- The graph displays a standard Cartesian coordinate system with labeled axes.
- The x-axis and y-axis both have a scale marked at intervals of 1.
- Circle B is centered at the point (3,-1) with a radius of 2 units.
To match Circle B to its equation, recall that the general form of the equation for a circle with center \((h, k)\) and radius \(r\) is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Given:
- The center \((h, k)\) for Circle B is (3, -1).
- The radius \(r\) is 2 units.
Substituting these values into the equation form gives:
\[
(x - 3)^2 + (y + 1)^2 = 2^2
\]
\[
(x - 3)^2 + (y + 1)^2 = 4
\]
#### Answer Choices:
A. \((x - 3)^2 + (y + 3)^2 = 4\)
B. \((x + 3)^2 - (y - 3)^2 = 4\)
C. \((x + 3)^2 + (y - 3)^2 = 4\)
D. \((x - 3)^2 - (y + 3)^2 = 4\)
Comparing these choices with our derived equation \((x - 3)^2 + (y + 1)^2 = 4\), none of the given options exactly match. The given options might likely have a typo or incorrect formatting.
However, to ensure accuracy in identifying what might have been intended, let's align closely and note the conceptual answer is:
\[
(x - 3)^2 + (y + 1)^2 = 4
\]
This educational content ensures understanding of both deriving the equation of a circle from a graph and matching it accurately to provided choices.](https://content.bartleby.com/qna-images/question/b294f3d7-c37e-4d19-872e-5bb2e2baac27/9f8f4402-956a-4611-8e27-36225302cb5a/l5cahim_processed.jpeg)
Transcribed Image Text:### Identifying the Equation of a Circle: An Educational Explanation
In this example, we need to determine which given equation correctly represents circle B shown on the graph.
#### Graph Details:
- The graph displays a standard Cartesian coordinate system with labeled axes.
- The x-axis and y-axis both have a scale marked at intervals of 1.
- Circle B is centered at the point (3,-1) with a radius of 2 units.
To match Circle B to its equation, recall that the general form of the equation for a circle with center \((h, k)\) and radius \(r\) is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Given:
- The center \((h, k)\) for Circle B is (3, -1).
- The radius \(r\) is 2 units.
Substituting these values into the equation form gives:
\[
(x - 3)^2 + (y + 1)^2 = 2^2
\]
\[
(x - 3)^2 + (y + 1)^2 = 4
\]
#### Answer Choices:
A. \((x - 3)^2 + (y + 3)^2 = 4\)
B. \((x + 3)^2 - (y - 3)^2 = 4\)
C. \((x + 3)^2 + (y - 3)^2 = 4\)
D. \((x - 3)^2 - (y + 3)^2 = 4\)
Comparing these choices with our derived equation \((x - 3)^2 + (y + 1)^2 = 4\), none of the given options exactly match. The given options might likely have a typo or incorrect formatting.
However, to ensure accuracy in identifying what might have been intended, let's align closely and note the conceptual answer is:
\[
(x - 3)^2 + (y + 1)^2 = 4
\]
This educational content ensures understanding of both deriving the equation of a circle from a graph and matching it accurately to provided choices.
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