In the first part of this paper has discussed about the
 basic properties of cyclide Dupin, and has gave some examples of
 their applications: three ways of solving the problem of Apollonius
 exclusively by means of compass and ruler, using identified properties
 cyclide Dupin, that is, given a classical solution of the problem.
 In the second of part of the work continued consideration of
 the properties of cyclide Dupin. Proposed and proved the possibility
 ask cyclide Dupin arbitrary ellipse as the center line of the
 forming a plurality of spheres and a sphere with the center belong -
 ing to the ellipse. Proved the adequacy of this information is used
 to build the cyclide Dupin. Geometrically proved that the focal line
 of cychlid are not that other, as curves of the second order. Given
 the graphical representation of the focal lines of cychlid. Shown
 polyconic compliance focal lines of cichlid of Dupin, which is
 considered in all four cases. The proposed formation of the hyperbolic surfaces of the fourth
 order with one or two primary curves of the second order, in this
 case ellipses. Apply sofocus this ellipse the hyperbola. Although the
 primary focus of the ellipse lying in the plane of the hoe, with the
 center coinciding with the origin of coordinates, is stationary, and
 the coordinate system rotates around the z axis. Then the points of
 intersection of the rotating coordinates x and y with a fixed ellipse
 specify new values for the major and minor axis of the ellipse with
 resultant changes in the form defocuses of the hyperbola. Although
 this modeling is not directly connected with Cychlidae Dupin, but
 clearly follows from the properties of its focal curves – curves of
 the second order. Withdrawn Equations of the surface and its throat.