Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. 9x2 – 14xy + 9y2 – 48 = 0 (a) Identify the resulting rotated conic. O ellipse O hyperbola O parabola (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.) (xp)² + 10(yp)² – 48 = 0 Need Help? Read It

Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation. 9x2 – 14xy + 9y2 – 48 = 0 (a) Identify the resulting rotated conic. O ellipse O hyperbola O parabola (b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.) (xp)² + 10(yp)² – 48 = 0 Need Help? Read It

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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Need Correct answers as soon as possible

Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the quadratic equation.
9x2 – 14xy + 9y2 – 48 = 0
(a) Identify the resulting rotated conic.
O ellipse
O hyperbola
O parabola
(b) Give its equation in the new coordinate system. (Use xp and yp as the new coordinates.)
(xp)² + 10(yp)² – 48 = 0
Need Help?
Read It

Find the matrix A of the quadratic form associated with the equation.
6x2 - 9xy - 6y2 + 6 = 0
6
-4.5
A =
-4.5
-6
Find the eigenvalues of A. (Enter your answers as a comma-separated list.)
(-7,7)
Find an orthogonal matrix P such that PTAP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.)
[1]
P =

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