Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Find the Center-Radius Form of the Equation of the Circle
#### Problem Statement:
Find the center-radius form of the equation of the circle described below. Then graph the circle.
- **Center:** \( \left( \sqrt{5}, \sqrt{2} \right) \)
- **Radius:** \( \sqrt{3} \)
#### Instructions:
Type the center-radius form of the equation of the circle described.
(Simplify your answer.)
#### Solution:
The center-radius form of the equation of a circle is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
Where \((h, k)\) is the center and \(r\) is the radius of the circle. For this specific problem:
- \( h = \sqrt{5} \)
- \( k = \sqrt{2} \)
- \( r = \sqrt{3} \)
Substitute these values into the center-radius form equation:
\[ (x - \sqrt{5})^2 + (y - \sqrt{2})^2 = (\sqrt{3})^2 \]
Simplify the equation:
\[ (x - \sqrt{5})^2 + (y - \sqrt{2})^2 = 3 \]
This is the equation of the circle in the center-radius form.
#### Graphing:
To graph this circle, plot the center at \( (\sqrt{5}, \sqrt{2}) \) on the coordinate plane and draw a circle with radius \( \sqrt{3} \).
#### Additional Resources:
- Watch our video on drawing circles in the coordinate plane.
- Practice similar problems to strengthen your understanding of conic sections.
(Note: Since the image does not contain any actual graphs or diagrams, a description of how to approach graphing has been provided for a more comprehensive educational experience.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb04437b-3f7e-4496-ba03-3a7f713d70b1%2Fb77d5c6e-1333-47d3-9df2-e40ce51d4e85%2Fcluufbm_processed.png&w=3840&q=75)
Transcribed Image Text:### Find the Center-Radius Form of the Equation of the Circle
#### Problem Statement:
Find the center-radius form of the equation of the circle described below. Then graph the circle.
- **Center:** \( \left( \sqrt{5}, \sqrt{2} \right) \)
- **Radius:** \( \sqrt{3} \)
#### Instructions:
Type the center-radius form of the equation of the circle described.
(Simplify your answer.)
#### Solution:
The center-radius form of the equation of a circle is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
Where \((h, k)\) is the center and \(r\) is the radius of the circle. For this specific problem:
- \( h = \sqrt{5} \)
- \( k = \sqrt{2} \)
- \( r = \sqrt{3} \)
Substitute these values into the center-radius form equation:
\[ (x - \sqrt{5})^2 + (y - \sqrt{2})^2 = (\sqrt{3})^2 \]
Simplify the equation:
\[ (x - \sqrt{5})^2 + (y - \sqrt{2})^2 = 3 \]
This is the equation of the circle in the center-radius form.
#### Graphing:
To graph this circle, plot the center at \( (\sqrt{5}, \sqrt{2}) \) on the coordinate plane and draw a circle with radius \( \sqrt{3} \).
#### Additional Resources:
- Watch our video on drawing circles in the coordinate plane.
- Practice similar problems to strengthen your understanding of conic sections.
(Note: Since the image does not contain any actual graphs or diagrams, a description of how to approach graphing has been provided for a more comprehensive educational experience.)
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