Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. 3x²8xy + 18y² - 44 = 0 (a) Identify the resulting rotated conic. O parabola hyperbola ellipse (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. 3x²8xy + 18y² - 44 = 0 (a) Identify the resulting rotated conic. O parabola hyperbola ellipse (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
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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![### Rotation of Axes: Principal Axes Theorem
**Objective:**
To perform a rotation of axes to eliminate the xy-term in the quadratic equation.
Consider the quadratic equation:
\[ 3x^2 - 8xy + 18y^2 - 44 = 0 \]
#### (a) Identifying the Resulting Rotated Conic
Identify the nature of the conic section resulting from the rotation.
- \(\bigcirc\) parabola
- \(\bigcirc\) hyperbola
- \(\bigcirc\) ellipse (Correct Answer)
*[A checkbox graphic indicates that "ellipse" is selected and marked as correct]*
#### (b) Equation in the New Coordinate System
Provide the equation of the conic section in the new coordinate system. Use \(xp\) and \(yp\) as the new coordinates.
*[A box placeholder is provided to input the transformed equation]*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F547c9318-b093-4c3c-ba93-abfa5f98a95a%2Fcaf47ebf-1ecb-437b-a9ca-1bb385811efb%2Fvud4kub_processed.png&w=3840&q=75)
Transcribed Image Text:### Rotation of Axes: Principal Axes Theorem
**Objective:**
To perform a rotation of axes to eliminate the xy-term in the quadratic equation.
Consider the quadratic equation:
\[ 3x^2 - 8xy + 18y^2 - 44 = 0 \]
#### (a) Identifying the Resulting Rotated Conic
Identify the nature of the conic section resulting from the rotation.
- \(\bigcirc\) parabola
- \(\bigcirc\) hyperbola
- \(\bigcirc\) ellipse (Correct Answer)
*[A checkbox graphic indicates that "ellipse" is selected and marked as correct]*
#### (b) Equation in the New Coordinate System
Provide the equation of the conic section in the new coordinate system. Use \(xp\) and \(yp\) as the new coordinates.
*[A box placeholder is provided to input the transformed equation]*
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