**Problem Description:**Find parametric equations for the following:- The circle of radius 2, centered at (0, 3, 0) in the plane $ y = 3 $, oriented counterclockwise as viewed from the positive y-axis.**Diagram Explanation:**The diagram shows a 3D coordinate system with the axes labeled $ x $, $ y $, and $ z $. The circle is depicted in the $ xz $-plane at $ y = 3 $, parallel to the xz-plane. The circle has a center at the point (0, 3, 0) and a radius of 2, lying on an imaginary plane located 3 units above the origin along the $ y $-axis. The circle's orientation is counterclockwise when viewed from the positive $ y $-axis.**Graphical Interpretation:**- **Axes:** - The $ x $-axis extends horizontally to the left. - The $ y $-axis extends vertically upward. - The $ z $-axis extends horizontally to the right and perpendicular to the $ x $-axis.- **Circle:** - The circle is represented as an ellipse due to the perspective view in the 3D coordinate system. Its true shape in its own plane $ y = 3 $ is a perfect circle.This visual aids in understanding how to find the parametric equations for the circle, given its specific orientation and location in three-dimensional space.

We should understand that y is going to be constant and is going to be 3 Now since r = 2 [given]…

Answered: Find parametric equations for each of…

Find parametric equations for each of the following. The circle of radius 2, centered at (0, 3, 0) in the plane y = 3, oriented counterclockwise as viewed from the positive y-axis.

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

**Problem Description:**

Find parametric equations for the following:

- The circle of radius 2, centered at (0, 3, 0) in the plane $ y = 3 $, oriented counterclockwise as viewed from the positive y-axis.

**Diagram Explanation:**

The diagram shows a 3D coordinate system with the axes labeled $ x $, $ y $, and $ z $. The circle is depicted in the $ xz $-plane at $ y = 3 $, parallel to the xz-plane. The circle has a center at the point (0, 3, 0) and a radius of 2, lying on an imaginary plane located 3 units above the origin along the $ y $-axis. The circle's orientation is counterclockwise when viewed from the positive $ y $-axis.

**Graphical Interpretation:**

- **Axes:**
- The $ x $-axis extends horizontally to the left.
- The $ y $-axis extends vertically upward.
- The $ z $-axis extends horizontally to the right and perpendicular to the $ x $-axis.

- **Circle:**
- The circle is represented as an ellipse due to the perspective view in the 3D coordinate system. Its true shape in its own plane $ y = 3 $ is a perfect circle.

This visual aids in understanding how to find the parametric equations for the circle, given its specific orientation and location in three-dimensional space.

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