New methods for constructing second-order curves

Abstract

This paper proposes a method for obtaining second-order curves, such as hyperbolas, using a graphical model of the biquadratic transformation. It should be noted that the modeling of curves using the method of biquadratic transformations of the plane allows us to obtain new curves of the fourth order. At the same time, it is recommended to use the new canonical biquadratic plane transformations developed in sections 2 and 3. Thus, we have considered a new construction of second-order curves, such as a hyperbola, using a graphical model of the transformation of the biquadratic transformation L₆ and L₈ with different positions of the prototype - a straight line relative to the OХ₂ axis.