Translate the equation below into standard form using completing the square. Then identify the center and raidus of the circle. đâ+8x + y2 -10y – 23 – 0 A. (x+4)² + (y-5)² = 64 (x+4)² + (-5)² =. = 41 center (4,-5) and radius is 64 center (4, -5) and radius is √√41 (x+4)² + (-5) = 23 191 20.0 center (4, -5) and radius is √23 center (-4, 5) and radius is 8 B. D. (x+4)² + (y-5)² = 64
Translate the equation below into standard form using completing the square. Then identify the center and raidus of the circle. đâ+8x + y2 -10y – 23 – 0 A. (x+4)² + (y-5)² = 64 (x+4)² + (-5)² =. = 41 center (4,-5) and radius is 64 center (4, -5) and radius is √√41 (x+4)² + (-5) = 23 191 20.0 center (4, -5) and radius is √23 center (-4, 5) and radius is 8 B. D. (x+4)² + (y-5)² = 64
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
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Help on #17
![### Problem 17
**Objective:** Translate the given equation into standard form using the method of completing the square. Then, identify the center and radius of the circle.
**Given Equation:**
\[ x^2 + 8x + y^2 - 10y - 23 = 0 \]
**Choices:**
**A.**
\[ (x + 4)^2 + (y - 5)^2 = 64 \]
- Center: \((4, -5)\)
- Radius: \(64\)
**B.**
\[ (x + 4)^2 + (y - 5)^2 = 23 \]
- Center: \((4, -5)\)
- Radius: \(\sqrt{23}\)
**C.**
\[ (x + 4)^2 + (y - 5)^2 = 41 \]
- Center: \((4, -5)\)
- Radius: \(\sqrt{41}\)
**D.**
\[ (x + 4)^2 + (y - 5)^2 = 64 \]
- Center: \((-4, 5)\)
- Radius: \(8\)
The correct choice has been marked as:
**Correct Answer:**
**C.**
\[ (x + 4)^2 + (y - 5)^2 = 41 \]
- Center: \((4, -5)\)
- Radius: \(\sqrt{41}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4904ad93-6dcc-43fa-9122-8f69394907f2%2Fea5c4298-cc8a-40bf-96bc-8620009c5feb%2Fo64mdd9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 17
**Objective:** Translate the given equation into standard form using the method of completing the square. Then, identify the center and radius of the circle.
**Given Equation:**
\[ x^2 + 8x + y^2 - 10y - 23 = 0 \]
**Choices:**
**A.**
\[ (x + 4)^2 + (y - 5)^2 = 64 \]
- Center: \((4, -5)\)
- Radius: \(64\)
**B.**
\[ (x + 4)^2 + (y - 5)^2 = 23 \]
- Center: \((4, -5)\)
- Radius: \(\sqrt{23}\)
**C.**
\[ (x + 4)^2 + (y - 5)^2 = 41 \]
- Center: \((4, -5)\)
- Radius: \(\sqrt{41}\)
**D.**
\[ (x + 4)^2 + (y - 5)^2 = 64 \]
- Center: \((-4, 5)\)
- Radius: \(8\)
The correct choice has been marked as:
**Correct Answer:**
**C.**
\[ (x + 4)^2 + (y - 5)^2 = 41 \]
- Center: \((4, -5)\)
- Radius: \(\sqrt{41}\)
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