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
Find the equation of the
![### Circle Equation Identification
#### Diagram Explanation:
The image displays a coordinate grid with a red circle plotted on it. The circle is centered at the point \((4, 3)\) and appears to have a radius extending to 2 units.
#### Question:
Given the circle's information in the diagram, determine the correct equation that represents the circle.
**Options:**
1. \((x - 4)^2 + (y - 3)^2 = 2\)
2. \((x + 4)^2 + (y + 3)^2 = 2\)
3. \((x - 4)^2 + (y - 3)^2 = 4\)
4. \((x + 4)^2 + (y + 3)^2 = 4\)
**Graphical Explanation:**
- **Center of the Circle:** The circle is centered at coordinates \((4, 3)\).
- **Radius:** The circle has a radius of 2 units, as determined from the circle's diameter measurement spanning 2 units outward from the center point.
**Identifying the Equation:**
The standard form of a circle's equation in a coordinate plane is:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
Where \((h, k)\) is the center of the circle, and \(r\) is the radius.
From the diagram, we have:
- Center \((h, k) = (4, 3)\)
- Radius \( r = 2 \)
Plugging these values into the standard form, we get:
\[ (x - 4)^2 + (y - 3)^2 = 2^2 \]
\[ (x - 4)^2 + (y - 3)^2 = 4 \]
Therefore, the correct equation for the circle is represented by **Option 3: \((x - 4)^2 + (y - 3)^2 = 4\)**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf693007-feb9-4e65-ba86-b1b16e800487%2Fe6543add-f6a6-45fe-a39f-7b6b03da5a76%2F90xvyu_processed.png&w=3840&q=75)
Transcribed Image Text:### Circle Equation Identification
#### Diagram Explanation:
The image displays a coordinate grid with a red circle plotted on it. The circle is centered at the point \((4, 3)\) and appears to have a radius extending to 2 units.
#### Question:
Given the circle's information in the diagram, determine the correct equation that represents the circle.
**Options:**
1. \((x - 4)^2 + (y - 3)^2 = 2\)
2. \((x + 4)^2 + (y + 3)^2 = 2\)
3. \((x - 4)^2 + (y - 3)^2 = 4\)
4. \((x + 4)^2 + (y + 3)^2 = 4\)
**Graphical Explanation:**
- **Center of the Circle:** The circle is centered at coordinates \((4, 3)\).
- **Radius:** The circle has a radius of 2 units, as determined from the circle's diameter measurement spanning 2 units outward from the center point.
**Identifying the Equation:**
The standard form of a circle's equation in a coordinate plane is:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
Where \((h, k)\) is the center of the circle, and \(r\) is the radius.
From the diagram, we have:
- Center \((h, k) = (4, 3)\)
- Radius \( r = 2 \)
Plugging these values into the standard form, we get:
\[ (x - 4)^2 + (y - 3)^2 = 2^2 \]
\[ (x - 4)^2 + (y - 3)^2 = 4 \]
Therefore, the correct equation for the circle is represented by **Option 3: \((x - 4)^2 + (y - 3)^2 = 4\)**.
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