Well I look at equation (2) in the paper on Bancroft's method and I clearly see that it is the equation of a sphere.  I see where you make reference to a book but I don't know what point you are trying to make.  But the bottom line is that we currently have two solution methods in the article, the least squares method and the Bancroft method.  Both of these methods use the equations of the surfaces of spheres.  Neither of these methods use the equations of a hyperboloid in any way.  Now if you people want to come up with a solution method which uses the equations for a hyperboloid then you should write a completely separate section.  The discussion of hyperboloids is completely useless for the solution methods we currently have documented.  The current solution methods works fine and I don't think you people can improve on it.