X^2 Y^2 Z^2-xy-yz-zx=0 132349-28. 1 X X^(2)-yz 1 Y Y^(2)-zx 1 Z Z^(2)-xy =0

 Here $\;p=\frac{\partial z}{\partial x}\;$ and $\;q=\frac{\partial z}{\partial y}$ Lagrange's equations are $ \begin{align} \frac{dx}{x^2yz} = \frac{dy}{y^2zx