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x^2+2xy+6xz+5y^2+2yz+a*z^2 canonical form

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 2      2      2                            
x  + 5*y  + a*z  + 2*x*y + 2*y*z + 6*x*z = 0
$$a z^{2} + x^{2} + 2 x y + 6 x z + 5 y^{2} + 2 y z = 0$$
a*z^2 + x^2 + 2*x*y + 6*x*z + 5*y^2 + 2*y*z = 0