Find the integral surface of PDEx^2p+y^2q+z^2=0 passes through the hyperbola xy=x+y,z=1

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Find the integral surface of PDE
x^2p+y^2q+z^2=0 passes through the hyperbola xy=x+y,z=1

integral surface of PDE
x^2p+y^2q+z^2=0 passes through the hyperbola xy=x+y,z=1
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