Please read questions instructions. Also, please state whether it is half or quarter or full or …. Etc sphere. Also, i want to know its orientation (in which direction the sphere will be). **Problem: Set of Points in 3D Space****Task**: Describe and sketch the following set of points defined by the conditions given below.**Equations and Conditions**:1. \((x + 2)^2 + y^2 + (z - 1)^2 = 9\)2. \(x \geq -2\), \(y \geq 0\), and \(z \geq 1\)**Explanation**:- The first equation \((x + 2)^2 + y^2 + (z - 1)^2 = 9\) represents a sphere in three-dimensional space with a center at \((-2, 0, 1)\) and a radius of 3. - The conditions \(x \geq -2\), \(y \geq 0\), and \(z \geq 1\) define the region of space the sphere occupies. Essentially, only the portions of the sphere that lie in the specified regions for \(x\), \(y\), and \(z\) can be considered for the sketch.**Conceptual Visualization**:- Visualize the entire sphere centered at \((-2, 0, 1)\), then restrict your visualization to only the points on and within the sphere meeting the given conditions of \(x\), \(y\), and \(z\).This type of problem helps in understanding how geometric shapes can be restricted to specific regions in three-dimensional space by using inequalities.

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Describe and sketch the following set of points defined by the following conditions. (x + 2)² + y² + (z-1)² = 9, x ≥-2 y ≥0) and z≥1

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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Question

Please read questions instructions. Also, please state whether it is half or quarter or full or …. Etc sphere. Also, i want to know its orientation (in which direction the sphere will be).

**Problem: Set of Points in 3D Space**

**Task**: Describe and sketch the following set of points defined by the conditions given below.

**Equations and Conditions**:

1. \((x + 2)^2 + y^2 + (z - 1)^2 = 9\)

2. \(x \geq -2\), \(y \geq 0\), and \(z \geq 1\)

**Explanation**:

- The first equation \((x + 2)^2 + y^2 + (z - 1)^2 = 9\) represents a sphere in three-dimensional space with a center at \((-2, 0, 1)\) and a radius of 3.

- The conditions \(x \geq -2\), \(y \geq 0\), and \(z \geq 1\) define the region of space the sphere occupies. Essentially, only the portions of the sphere that lie in the specified regions for \(x\), \(y\), and \(z\) can be considered for the sketch.

**Conceptual Visualization**:

- Visualize the entire sphere centered at \((-2, 0, 1)\), then restrict your visualization to only the points on and within the sphere meeting the given conditions of \(x\), \(y\), and \(z\).

This type of problem helps in understanding how geometric shapes can be restricted to specific regions in three-dimensional space by using inequalities.

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