Curves have always been part geometry. Initially, there were lines and circle, then it was added to a conic section and later, with the advent of analytic geometry, they added more complex curves. Particularly in a number of lines are algebraic curves that are described by algebraic equations. Curves found application mostly in mechanics. Today algebraic curves used in engineering and in mathematics, in number theory, knot theory, computer science, criminology, etc. With the bringing to account of complex numbers became possible to consider curves in the complex plane. It has expanded the horizons of geometry and enriched their knowledge on curves, particularly on algebraic curves. Our goal is to give a geometric picture of the foci of algebraic curves clearly show the position of the foci in the plane, show how the number of foci associated with a class curve. The solution of this problem we see in the application we have developed ways to visualize imaginary images to the study of foci and focal centers of algebraic curves. This article explains the concept of the foci of algebraic curves shows the basic principle of the curve-theory and offers a method for the identification of the foci. The geometric picture of the foci is shown in a diagram, which is putted together from two tables. One table shows the real curve with her foci, the other table shows an imaginary cut of the curve, on which the isotropic line contacts the cut and under them intersects in a real point. The point is a focal point of the real curve. This project shows 16 diagrams for conic, cubes and quadrics.

A one-parameter family of algebraic curves has an envelope line, which may be imaginary in certain cases. Jakob Steiner was right, considering the imaginary images as creation of analysis. In the analysis a real number is just a part of a complex number and in certain conditions the initial real values can give an imaginary result. But Steiner was wrong in denying the imaginary images in geometry. The geometry, in contrast to the single analytical space exists in several spaces: Euclidean geometry operates only on real figures valid and does not contain imaginary figures by definition; pseudo-Euclidean geometry operates on imaginary images and constructs their images, taking into account its own features. Geometric space is complex and each geometric object in it is the complex one, consisting of the real figure (core) having the "aura" of an imaginary extension. Thus, any analytical figure of the plane is present at every point of the plane or by its real part or by its imaginary extension. Would the figure’s imaginary extension be visible or not depends on the visualization method, whether the image has been assumed on superimposed epures – the Euclideanpseudo-Euclidean plane, or the image has been traditionally assumed only in the Euclidean plane. In this paper are discussed cases when a family of algebraic curves has an envelope, and is given an answer to a question what means cases of complete or partial absence of the envelope for the one-parameter family of curves. Casts some doubt on widely known categorical st