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
Can u help me with these two?
![**Determining the Standard Equation of a Circle**
When provided with the center and radius of a circle, the standard equation of the circle can be derived using the formula:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) represents the center of the circle and \(r\) represents the radius.
**Examples:**
1. **Problem 9:**
- **Given:** Center = \((2, 3)\); Radius = \(5\)
- **Solution:** Substituting the given values into the standard equation formula:
\[
(x - 2)^2 + (y - 3)^2 = 5^2
\]
This simplifies to:
\[
(x - 2)^2 + (y - 3)^2 = 25
\]
2. **Problem 10:**
- **Given:** Center = \((0, -1)\); Radius = \(\sqrt{7}\)
- **Solution:** Substituting the given values into the standard equation formula:
\[
(x - 0)^2 + (y + 1)^2 = (\sqrt{7})^2
\]
This simplifies to:
\[
x^2 + (y + 1)^2 = 7
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd02dd32a-1cbf-44a4-af8e-a4a327187a34%2F66da565c-aa65-4d35-832e-1b170e579403%2Fatbqb5_processed.png&w=3840&q=75)
Transcribed Image Text:**Determining the Standard Equation of a Circle**
When provided with the center and radius of a circle, the standard equation of the circle can be derived using the formula:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) represents the center of the circle and \(r\) represents the radius.
**Examples:**
1. **Problem 9:**
- **Given:** Center = \((2, 3)\); Radius = \(5\)
- **Solution:** Substituting the given values into the standard equation formula:
\[
(x - 2)^2 + (y - 3)^2 = 5^2
\]
This simplifies to:
\[
(x - 2)^2 + (y - 3)^2 = 25
\]
2. **Problem 10:**
- **Given:** Center = \((0, -1)\); Radius = \(\sqrt{7}\)
- **Solution:** Substituting the given values into the standard equation formula:
\[
(x - 0)^2 + (y + 1)^2 = (\sqrt{7})^2
\]
This simplifies to:
\[
x^2 + (y + 1)^2 = 7
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning