Abstract:
The article describes setting the families of confocal ellipses and hyperbolas and studying their properties through the GeoGebra mathematical package in the course "Analytic geometry" under the topic "Second-order curve" by the students of a technical college. The primary purpose of the article is to demonstrate the integration of modern information technology into the process of teaching higher mathematics. Using the built-in tools and commands of the GeoGebra environment, the setting and construction of confocal ellipses and hyperbolas are shown step-by-step. Using the dynamic drawings, the author considers the process of "transformation" of one conic into another at different values of the specified parameters. Relying on the properties of a tangent to a second-order curve, the author found and analyzed that the confocal ellipse and the hyperbola intersect at a right angle. The last result is considered for various cases of the mutual arrangement of curves and tangents at the point of their intersection. All the results obtained are justified strictly mathematically.
Keywords:GeoGebra, GeoGebra, teaching mathematics, second-order curves, ellipse, hyperbola, tangents to conics, optical properties of conics, confocal conics, angles between curves.
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