Unformatted text preview: loci described above, in the new coordinate system, displaced so the origin moves to ξ 1 = − α/ 2 λ 1 , ξ 2 = − β/ 2 λ 2 . We illustrate with two examples. First, consider the curve 4 xy − 6 x + 2 y = 4 . The quadratic form Q ( x,y ) = 4 xy has matrix representative A = [ Q ] = b 0 2 2 0 B with eigenvalues λ 1 = 2 , λ 2 = − 1 and corresponding unit eigenvectors −→ u 1 = p 1 √ 2 , 1 √ 2 P −→ u 2 = p − 1 √ 2 , 1 √ 2 P ; thus c = s = 1 √ 2...
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 Spring '08
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 Calculus, Linear Algebra, Quadratic equation

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