8 m A. 55 m² B. 110 m² D. 44 m² Translate the equation below into standard form using completing the square. Then identify the center and raidus of the circle. x² + 8x+y²-10y - 23 = 0 Ere A. (x+4)² + (y-5)² - 64 A = (x+4)² + (y-5)² = 41 √√41 center (4,-5) and radius is no 38A his elu B. (x+4)² + (y-5)² - 23 = = D. (x+4)² + (y-5)² = 64 center (4,-5) and radius is √√23 center (-4, 5) and radius is 8 ng the figure below, find the measure of angle A. Round your answer to the nearest deg wing is not to scale. center (4, -5) and radius is 64 220 m²
8 m A. 55 m² B. 110 m² D. 44 m² Translate the equation below into standard form using completing the square. Then identify the center and raidus of the circle. x² + 8x+y²-10y - 23 = 0 Ere A. (x+4)² + (y-5)² - 64 A = (x+4)² + (y-5)² = 41 √√41 center (4,-5) and radius is no 38A his elu B. (x+4)² + (y-5)² - 23 = = D. (x+4)² + (y-5)² = 64 center (4,-5) and radius is √√23 center (-4, 5) and radius is 8 ng the figure below, find the measure of angle A. Round your answer to the nearest deg wing is not to scale. center (4, -5) and radius is 64 220 m²
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
![### Understanding Circles and Their Equations
In this lesson, we will explore how to translate the general equation of a circle into its standard form by completing the square. We'll then identify the circle's center and radius based on this standard form.
#### Problem Statement:
**Given Equation:**
\[ x^2 + 8x + y^2 - 10y = 23 \]
Translate this equation into standard form using the method of completing the square. Then, identify the center and radius of the circle.
#### Solution Steps:
1. **Rewrite Equation:**
Start with the given equation:
\[ x^2 + 8x + y^2 - 10y = 23 \]
2. **Group x and y terms:**
\[ (x^2 + 8x) + (y^2 - 10y) = 23 \]
3. **Complete the Square:**
For \(x\) terms:
\[ x^2 + 8x \]
- Take half of 8, square it: \(\left(\frac{8}{2}\right)^2 = 16\)
- Add and subtract 16 inside the group:
\[ (x^2 + 8x + 16 - 16) \]
For \(y\) terms:
\[ y^2 - 10y \]
- Take half of -10, square it: \(\left(\frac{-10}{2}\right)^2 = 25\)
- Add and subtract 25 inside the group:
\[ (y^2 - 10y + 25 - 25) \]
Adding these adjustments into the original equation:
\[ (x^2 + 8x + 16) + (y^2 - 10y + 25) = 23 + 16 + 25 \]
Simplifies to:
\[ (x + 4)^2 + (y - 5)^2 = 64 \]
4. **Standard Form of the Circle:**
The standard form is:
\[ (x + 4)^2 + (y - 5)^2 = 64 \]
5. **Identify Center and Radius:**
- Center \((h, k)\): \((4, -5)\)
- Radius \( r \): \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5a061b4-0108-4a51-81fc-44207999c893%2F02c9536b-09ab-493f-89d9-3afe402381b9%2Fhgk7k8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Circles and Their Equations
In this lesson, we will explore how to translate the general equation of a circle into its standard form by completing the square. We'll then identify the circle's center and radius based on this standard form.
#### Problem Statement:
**Given Equation:**
\[ x^2 + 8x + y^2 - 10y = 23 \]
Translate this equation into standard form using the method of completing the square. Then, identify the center and radius of the circle.
#### Solution Steps:
1. **Rewrite Equation:**
Start with the given equation:
\[ x^2 + 8x + y^2 - 10y = 23 \]
2. **Group x and y terms:**
\[ (x^2 + 8x) + (y^2 - 10y) = 23 \]
3. **Complete the Square:**
For \(x\) terms:
\[ x^2 + 8x \]
- Take half of 8, square it: \(\left(\frac{8}{2}\right)^2 = 16\)
- Add and subtract 16 inside the group:
\[ (x^2 + 8x + 16 - 16) \]
For \(y\) terms:
\[ y^2 - 10y \]
- Take half of -10, square it: \(\left(\frac{-10}{2}\right)^2 = 25\)
- Add and subtract 25 inside the group:
\[ (y^2 - 10y + 25 - 25) \]
Adding these adjustments into the original equation:
\[ (x^2 + 8x + 16) + (y^2 - 10y + 25) = 23 + 16 + 25 \]
Simplifies to:
\[ (x + 4)^2 + (y - 5)^2 = 64 \]
4. **Standard Form of the Circle:**
The standard form is:
\[ (x + 4)^2 + (y - 5)^2 = 64 \]
5. **Identify Center and Radius:**
- Center \((h, k)\): \((4, -5)\)
- Radius \( r \): \(
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