Write the equation for a circle that is centered at (0,0) and passes through the point (-3,5). A x²-y²=34 B (x+3)² + (x - 5)² = 2 C (x-3)² + (x + 5)² = 34 D x² + y² = 34
Write the equation for a circle that is centered at (0,0) and passes through the point (-3,5). A x²-y²=34 B (x+3)² + (x - 5)² = 2 C (x-3)² + (x + 5)² = 34 D x² + y² = 34
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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![### Question 4
**Write the equation for a circle that is centered at (0,0) and passes through the point (-3,5).**
#### Options:
A. \( x^2 - y^2 = 34 \)
B. \( (x + 3)^2 + (x - 5)^2 = 2 \)
C. \( (x - 3)^2 + (x + 5)^2 = 34 \)
D. \( x^2 + y^2 = 34 \)
### Explanation:
To find the equation of a circle centered at the origin \((0,0)\) and passing through a particular point, we use the standard form of the equation of a circle:
\[ x^2 + y^2 = r^2 \]
where \((x, y)\) is any point on the circle and \(r\) is the radius.
To find the radius \(r\), we can substitute the coordinates of the given point \((-3,5)\) into the equation:
\[ (-3)^2 + 5^2 = r^2 \]
\[ 9 + 25 = r^2 \]
\[ 34 = r^2 \]
Thus, the equation of the circle is:
\[ x^2 + y^2 = 34 \]
So, the correct answer is:
**Option D: \( x^2 + y^2 = 34 \).**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8182640d-a39f-4906-bb1d-1d29c4c23cc2%2Ff856f571-6110-437e-a8c0-5d6fd03542b4%2Fd5qxdxd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 4
**Write the equation for a circle that is centered at (0,0) and passes through the point (-3,5).**
#### Options:
A. \( x^2 - y^2 = 34 \)
B. \( (x + 3)^2 + (x - 5)^2 = 2 \)
C. \( (x - 3)^2 + (x + 5)^2 = 34 \)
D. \( x^2 + y^2 = 34 \)
### Explanation:
To find the equation of a circle centered at the origin \((0,0)\) and passing through a particular point, we use the standard form of the equation of a circle:
\[ x^2 + y^2 = r^2 \]
where \((x, y)\) is any point on the circle and \(r\) is the radius.
To find the radius \(r\), we can substitute the coordinates of the given point \((-3,5)\) into the equation:
\[ (-3)^2 + 5^2 = r^2 \]
\[ 9 + 25 = r^2 \]
\[ 34 = r^2 \]
Thus, the equation of the circle is:
\[ x^2 + y^2 = 34 \]
So, the correct answer is:
**Option D: \( x^2 + y^2 = 34 \).**
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