Engineering Calculus Notes 409

Engineering Calculus Notes 409 - 397 3.10. QUADRATIC CURVES...

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Unformatted text preview: 397 3.10. QUADRATIC CURVES AND SURFACES ξ2 − √ 2 ξ1 − y 1 √ 2 y= 3 2 x 1 x = −2 Figure 3.30: The curve 4xy − 6x + 2y = 4 has matrix representative A = [ Q] = with eigenvalues λ1 = 2, → −= u1 → −= u2 1 −1 −1 1 λ2 = 0 and corresponding unit eigenvectors 1 1 √ , −√ 2 2 1 1 √ ,√ ; 2 2 thus 1 c= √ 2 1 s = −√ 2 and x−y ξ1 = √ 2 x+y ξ2 = √ 2 ...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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