Let A be a symmetric 2 X 2 matrix and let k be a scalar. Prove that the graph of the quadratic equation xT Ax = k is ,an ellipse, circle, or imaginary conic if k ≠0 and det A > 0

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 6AEXP
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Let A be a symmetric 2 X 2 matrix and let k be a scalar. Prove that the graph of the quadratic equation xT Ax = k is ,an ellipse, circle, or imaginary conic if k ≠0 and det A > 0

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