Perform a rotation of axes to eliminate the xy-term. (Use x, and Y2 for the rotated coordinates.) xy - 8x - 4y = 0
Perform a rotation of axes to eliminate the xy-term. (Use x, and Y2 for the rotated coordinates.) xy - 8x - 4y = 0
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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![**Problem Statement:**
Perform a rotation of axes to eliminate the xy-term. (Use \( x_2 \) and \( y_2 \) for the rotated coordinates.)
**Equation:**
\[ xy - 8x - 4y = 0 \]
**Instructions:**
To eliminate the xy-term, apply a rotation of axes. This involves transforming the original coordinates \((x, y)\) to new coordinates \((x_2, y_2)\). The process typically involves identifying an appropriate angle of rotation such that the new axes do not include the cross-product term in the equation.
**Visual Explanation:**
There is a blank space to perform these calculations and note down intermediate steps, such as identifying the angle of rotation, applying trigonometric relationships, and rewriting the equation in the new coordinate system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08594285-cc6b-4718-bdd1-7a3127ce35f5%2Fd2f88025-002f-4bd0-9ace-469918dfa8cd%2Flyqoti_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Perform a rotation of axes to eliminate the xy-term. (Use \( x_2 \) and \( y_2 \) for the rotated coordinates.)
**Equation:**
\[ xy - 8x - 4y = 0 \]
**Instructions:**
To eliminate the xy-term, apply a rotation of axes. This involves transforming the original coordinates \((x, y)\) to new coordinates \((x_2, y_2)\). The process typically involves identifying an appropriate angle of rotation such that the new axes do not include the cross-product term in the equation.
**Visual Explanation:**
There is a blank space to perform these calculations and note down intermediate steps, such as identifying the angle of rotation, applying trigonometric relationships, and rewriting the equation in the new coordinate system.
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