Problem research of display the orthogonal projection of four dimensional hypersurface defined by the equation in an implicit form one and two hyperplane. To communicate and bypass hypersurface Discriminants assumes that the hypersurface of the two-parameter family of two-dimensional display received surfaces in five-dimensional space. The analysis of kriminant four dimensional hypersurface orthogonal projection onto the coordinate hyperplane in two coordinate axes. The intersection of three dimensional hypersurfaces axiom (kriminant) defines a two-dimensional surface that is the envelope of the two-parameter family of two-dimensional surfaces. Are the necessary and sufficient conditions of existence of this envelope.
The results obtained are used to study the Discriminants four-dimensional hypersurface, the display of two-parameter family of spheres in a five-dimensional space.
Keywords: a family of surfaces, hypersurface, envelope, the display features, а discriminant.