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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![## 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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