What is the equation of the circle with the given parameters? Center: (13, -13) Radius: 4 O (r +13)? + (y – 13) = 42 O (r+ 13) + (y- 13) = 4 O (2- 13)2 + (y + 13)2 42 O (2 13) + (y + 13) 4
What is the equation of the circle with the given parameters? Center: (13, -13) Radius: 4 O (r +13)? + (y – 13) = 42 O (r+ 13) + (y- 13) = 4 O (2- 13)2 + (y + 13)2 42 O (2 13) + (y + 13) 4
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![**Title: Understanding Circle Equations**
**What is the equation of the circle with the given parameters?**
**Center:** (13, -13)
**Radius:** 4
**Multiple Choice Options:**
1. \( (x + 13)^2 + (y - 13)^2 = 4^2 \)
2. **\( (x - 13)^2 + (y + 13)^2 = 4 \)** *(Correct Answer)*
3. \( (x - 13)^2 + (y + 13)^2 = 4^2 \)
4. \( (x - 13)^2 + (y + 13) = 4 \)
### Analysis:
Consider the general form of a circle’s equation:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
Where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius of the circle.
Given:
- Center (h, k) = (13, -13)
- Radius (r) = 4
When substituting the given parameters into the general equation:
\[ (x - 13)^2 + (y + 13)^2 = 4^2 \]
This simplifies to:
\[ (x - 13)^2 + (y + 13)^2 = 16 \]
**Explanation of Options:**
1. \( (x + 13)^2 + (y - 13)^2 = 4^2 \) - This option incorrectly places the center at (-13, 13) and correctly squares the radius to 16.
2. **\( (x - 13)^2 + (y + 13)^2 = 4 \)** - This is incorrect because it has the center correct but does not square the radius.
3. \( (x - 13)^2 + (y + 13)^2 = 4^2 \) - This is the correct equation as it correctly places the center and squares the radius.
4. \( (x - 13)^2 + (y + 13) = 4 \) - This is incorrect. It both lacks the correct squaring of terms and misplaces the operators.
Thus, the correct equation for the circle is:
\[ (x - 13)^2 + (y + 13)^2 = 16 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34dbf93a-185c-4522-bbbf-f73f18b87311%2Fce1d50a3-a0a5-4490-8eaf-b8dae2451b11%2F82lh38m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Circle Equations**
**What is the equation of the circle with the given parameters?**
**Center:** (13, -13)
**Radius:** 4
**Multiple Choice Options:**
1. \( (x + 13)^2 + (y - 13)^2 = 4^2 \)
2. **\( (x - 13)^2 + (y + 13)^2 = 4 \)** *(Correct Answer)*
3. \( (x - 13)^2 + (y + 13)^2 = 4^2 \)
4. \( (x - 13)^2 + (y + 13) = 4 \)
### Analysis:
Consider the general form of a circle’s equation:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
Where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius of the circle.
Given:
- Center (h, k) = (13, -13)
- Radius (r) = 4
When substituting the given parameters into the general equation:
\[ (x - 13)^2 + (y + 13)^2 = 4^2 \]
This simplifies to:
\[ (x - 13)^2 + (y + 13)^2 = 16 \]
**Explanation of Options:**
1. \( (x + 13)^2 + (y - 13)^2 = 4^2 \) - This option incorrectly places the center at (-13, 13) and correctly squares the radius to 16.
2. **\( (x - 13)^2 + (y + 13)^2 = 4 \)** - This is incorrect because it has the center correct but does not square the radius.
3. \( (x - 13)^2 + (y + 13)^2 = 4^2 \) - This is the correct equation as it correctly places the center and squares the radius.
4. \( (x - 13)^2 + (y + 13) = 4 \) - This is incorrect. It both lacks the correct squaring of terms and misplaces the operators.
Thus, the correct equation for the circle is:
\[ (x - 13)^2 + (y + 13)^2 = 16 \
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