I have equations for saddle-shaped surface (likely hyperbolic paraboloid) in $3D$ space. Example image
In such cases, I want to know the equations of two lines which are,
- Lies on the surface of the given equation
- has constant $z$
For example, for the following values,
$z = a + bx + cy + dxy+ex^2+fy^2$
$ a = 1.3907,$
$b = -0.087591,$
$c = -0.25811,$
$d = 0.033397,$
$e = 0.0027985,$
$f = 0.00089385 $
The shape of the surface and such line would be like this image ( wolfram alpha link for the surface )
How can I get an equation of such a line?