Mathematical software application for an analytical geometry problem with a parameter solving and visualization

In this issue we study the possibility of mathematical software usage for analytical geometry with parameters problem solving. A review of Russian and foreign sources has shown that, despite the variety of mathematical software applications, they are rarely used to solve problems with parameters. The purpose of the study was to test the possibility of a mathematical package usage to solve problems with parameters, which will allow to avoid arithmetic and other errors and to obtain a tool for generating different variants of the same problem and a template for students’ solutions checking. Materials and methods. We used Mathcad 15.0 environment for the straight line and an ellipse with a variable symmetry center ordinate relative position determination. First analytical solution of the relative position of a straight line and a second-order curve with a parameter problem is based on the number of curves’ common points and their coordinates functional dependence on the parameter analysis. Second one is based on the point of contact coordinates determination using the equality of the straight line angular coefficients and curve tangent at the point of contact. Results. In this study it was established that Mathcad allows to implement both analytical methods and directly find the expressions for the coordinates of the depending on the parameter by solving a system of nonlinear equations and then to exam them for the set of real numbers belonging. Conclusion. Our research ascertains that Mathcad can be implemented for visualization and various solutions of analytical geometry with a parameter problem. Mathcad solution can be used to generate a set of different variants of the same problem with a rational number results, to verify students’ problem solutions, and also as an example of correct solution.