Answered: (1) Consider the conic section 3x7 +…

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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(b) Diagonalize A; the matrix that implements the diagonalization must be a (real) orthogonal matrix.

(c) Determine the principle axes of the conic (their equations must be presented) and its equation with respect to a new coordinate system whose axes are the principle axes of the conic.

(d) State whether the conic is an ellipse, a hyperbola, or a parabola; and sketch it.

(1) Consider the conic section 3x7 + 4x12 + 6x3 = 14.

(a)
Express the equation in the form XTAX :
14 where A is a real symmetric
matrix and
x - (:)
X2

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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