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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 Spring '08
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 Calculus, Linear Algebra, Eigenvectors, Vectors, representative, unit eigenvectors, matrix representative, QUADRATIC CURVES

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