x^2+y^2+1

This is an equation of a 3D surface called a "hyperboloid of one sheet". It is a smooth, continuous surface that extends infinitely in all directions. The surface is shaped like a saddle, with two "arms" that curve downward and away from each other, and a "saddle point" in the middle where the surface is tangent to the xy-plane. The equation does not define any particular point on the surface, but rather describes the entire surface as a whole.