In an appropriately selected cartesian coordinate system, the hyperbolic paraboloid has the equation "

"x^2 / a^2 - y^2 / b^2 = 2*z.""

The model represents the two systems of planes parallel to the planes x/a + y/b = 0 and x/a - y/b = 0, the latter planes each containing the z-axis and one of the intersection lines of the plane z = 0 with the paraboloid. The two systems of parallel planes intersect the paraboloid in the both systems of generating lines. The model is suited to illustrate that the paraboloid may be moved in itself.

The hyperbolic paraboloid is a ruled surface of the second order (regulus). Besides the hyperbolic paraboloid is als a hyperboloid of one sheet a regulus. Each regulus has two families of straight generatrices. With hyperbolic paraboloid to each family belongs a direction plane. The planes in the model are parallel to the direction planes. The axis of the hyperbolic paraboloid is parallel to both of the direction plane.