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
![### Circle Equations from Given Center and Radius
The equation of a circle in standard form is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) represents the center of the circle and \(r\) is the radius.
Given the following conditions, find the equations of the circles:
1. **Center: (0,0) and Radius: \( \sqrt{2} \)**
2. **Center: (-1, -1) and Radius: 4**
**Find the equation for each:**
a. **Center: (0,0) and Radius: \( \sqrt{2} \)**
**The equation is:**
\[ \_\_\_\_\_\_\_ \]
(Type your answer in standard form.)
b. **Center: (-1, -1) and Radius: 4**
**The equation is:**
\[ \_\_\_\_\_\_\_ \]
(Type your answer in standard form.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6506383-1f6c-4925-93a1-d439ea45d460%2Fdd3f4217-a856-4df9-930b-8f6dda60a113%2F4n0n6yk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Circle Equations from Given Center and Radius
The equation of a circle in standard form is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) represents the center of the circle and \(r\) is the radius.
Given the following conditions, find the equations of the circles:
1. **Center: (0,0) and Radius: \( \sqrt{2} \)**
2. **Center: (-1, -1) and Radius: 4**
**Find the equation for each:**
a. **Center: (0,0) and Radius: \( \sqrt{2} \)**
**The equation is:**
\[ \_\_\_\_\_\_\_ \]
(Type your answer in standard form.)
b. **Center: (-1, -1) and Radius: 4**
**The equation is:**
\[ \_\_\_\_\_\_\_ \]
(Type your answer in standard form.)
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