Find the center and radius of the sphere: 3x² + 3y² + 3z² -6x - 12y + 18z + 150 O Center (1, 2, -3); Radius = 3 Center (1, 2, -3); Radius = 1 Center (-1, -2, 3); Radius = 1 O Center (-1, -2, 3); Radius = √3 O none of these
Find the center and radius of the sphere: 3x² + 3y² + 3z² -6x - 12y + 18z + 150 O Center (1, 2, -3); Radius = 3 Center (1, 2, -3); Radius = 1 Center (-1, -2, 3); Radius = 1 O Center (-1, -2, 3); Radius = √3 O none of these
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 70E
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Question
![## Determine the Center and Radius of a Sphere
Consider the equation for the sphere:
\[ 3x^2 + 3y^2 + 3z^2 - 6x - 12y + 18z + 15 = 0 \]
### Multiple Choice Answers:
1. **Center (1, 2, -3); Radius = 3**
2. **Center (1, 2, -3); Radius = 1**
3. **Center (-1, -2, 3); Radius = 1**
4. **Center (-1, -2, 3); Radius =** \(\sqrt{3}\)
5. **None of these**
Use the coordinates and radius provided in each option to correctly identify the center and radius of the sphere defined by the given equation.
### Explanation of Graphs/Diagrams:
In this question, there are no graphical elements or diagrams accompanying the problem. The task involves purely algebraic manipulation to identify the correct center and radius from the provided equation.
**Tip**: To find the center and radius, you might want to consider completing the square for the variables \(x\), \(y\), and \(z\) in the equation, then compare the resulting format with the general equation of a sphere \((x - h)^2 + (y - k)^2 + (z - l)^2 = r^2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55815b3c-2575-4201-a9dc-5a4b41a14c1d%2Ff9283bf2-9e5b-4bc0-a54d-68b1d18ffb4c%2Fcmy71pc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Determine the Center and Radius of a Sphere
Consider the equation for the sphere:
\[ 3x^2 + 3y^2 + 3z^2 - 6x - 12y + 18z + 15 = 0 \]
### Multiple Choice Answers:
1. **Center (1, 2, -3); Radius = 3**
2. **Center (1, 2, -3); Radius = 1**
3. **Center (-1, -2, 3); Radius = 1**
4. **Center (-1, -2, 3); Radius =** \(\sqrt{3}\)
5. **None of these**
Use the coordinates and radius provided in each option to correctly identify the center and radius of the sphere defined by the given equation.
### Explanation of Graphs/Diagrams:
In this question, there are no graphical elements or diagrams accompanying the problem. The task involves purely algebraic manipulation to identify the correct center and radius from the provided equation.
**Tip**: To find the center and radius, you might want to consider completing the square for the variables \(x\), \(y\), and \(z\) in the equation, then compare the resulting format with the general equation of a sphere \((x - h)^2 + (y - k)^2 + (z - l)^2 = r^2\).
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