The complete solution of the equation \(\left( {\frac{{\partial z}}{{\partial x}}.\frac{{\partial z}}{{\partial y}} - \frac{{\partial z}}{{\partial x}} - \frac{{\partial z}}{{\partial y}}} \right)\left( {z - x\frac{{\partial z}}{{\partial x}} - y\frac{{\partial z}}{{\partial y}}} \right) = \frac{{\partial z}}{{\partial x}}.\frac{{\partial z}}{{\partial y}}\) is
1
\(z = ax - by + \frac{{ab}}{{ab - a - b}}\)
2
\(z = ax + by + \frac{{ab}}{{ab + a + b}}\)
3
\(z = ax - by + \frac{{ab}}{{ab + a + b}}\)
4
\(z = ax + by + \frac{{ab}}{{ab - a - b}}\)