Use the Principal Axes The

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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7.4: Applications of Eigenvalues

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Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation.
2x2 + 4xy + 2y² + 6V2x + 2/2y + 9 = 0
(a) Identify the resulting rotated conic.
ellipse
parabola
O hyperbola
(b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
Transcribed Image Text:Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. 2x2 + 4xy + 2y² + 6V2x + 2/2y + 9 = 0 (a) Identify the resulting rotated conic. ellipse parabola O hyperbola (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
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