Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. 10x? – 18xy + 10y2 – 45 = 0 (a) Identify the resulting rotated conic. O parabola hyperbola O 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. 10x? – 18xy + 10y2 – 45 = 0 (a) Identify the resulting rotated conic. O parabola hyperbola O 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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![**Title: Understanding Rotation of Axes in Conic Sections**
Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation.
\[ 10x^2 - 18xy + 10y^2 - 45 = 0 \]
(a) Identify the resulting rotated conic.
- ○ Parabola
- ○ Hyperbola
- ○ Ellipse
(b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
[Input Box for Equation]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f30608e-bf31-4a49-92e6-e964952b6a83%2F210a107b-d471-4e88-8982-9da9f5bee5b3%2Ferudo7f_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Rotation of Axes in Conic Sections**
Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation.
\[ 10x^2 - 18xy + 10y^2 - 45 = 0 \]
(a) Identify the resulting rotated conic.
- ○ Parabola
- ○ Hyperbola
- ○ Ellipse
(b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
[Input Box for Equation]
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