ЗАДАЧИ ЗА ДВОЙКИ КРИВИ ОТ ВТОРА СТЕПЕН В ПРОФИЛИРАНАТА ПОДГОТОВКА ПО МАТЕМАТИКА

Даниела Йорданова Георгиева¹, Марта Костадинова Теофилова²
¹Природо-математическа гимназия „Академик Боян Петканчин“, Хасково
²Пловдивски университет „Паисий Хилендарски“, Пловдив

PROBLEMS FOR PAIRS OF SECOND-DEGREE CURVES IN THE PROFILED TRAINING IN MATHEMATICS

Daniela Yordanova Georgieva¹, Marta Kostadinova Teofilova²

¹Boyan Petkanchin High School of Natural Sciences and Mathematics, Haskovo
²Plovdiv University „Paisii Hilendarski“, Plovdiv

* Авторите изказват благодарност към проф. д-р Пенка Рангелова за идеята на настоящата статия, както и за ценните съвети и напътствия при нейното разработване. Първият автор благодари на проект МУПД25-ФМИ-015 към ФНИ на Пловдивския университет „Паисий Хилендарски“.

Abstract: In the profiled mathematics preparation, students study the analytical definition of four seconddegree curves – circle, ellipse, hyperbola and parabola, which are collectively called conic sections, since they are obtained when a rotational conical surface intersects a plane at different angles between the axis of the cone and the plane. In the 11th grade, students are introduced to the definitions and equations of the four curves and study their basic properties and elements – center, axes, vertices, foci, directrix, etc. . In the 12th grade, students consider tangents to second-degree curves and learn their equations. In the educational literature, quite a few problems are proposed for each of the conic sections separately, but problems combining two or more curves are less common. The purpose of this work is to offer ideas for conducting a generalized lesson on the study material for conic sections with problems for two or more second-degree curves, which are interconnected by relations for some of their elements. We believe that solving such problems helps students in a deeper understanding of the educational material, as well as in the consolidation and permanent mastery of knowledge and skills for working with the apparatus of analytical geometry. In the work, we offer problems on the material for second-degree curves, studied in the profiled preparation in the 11th grade.

Keywords: ellipse, hyperbola, parabola, circle, second degree curve

References:

1. Tonov, I., I. Sharkova, M. Hristova, Matematika za 11. klas – profilirana podgotovka, Regalia 6, Sofia, 2020, ISBN 978-954-745-330-2.
2. Stewart, J., Essential Calculus, 2nd ed., Cengage Learning, 2012, ISBN · 9781133112297
3. Sobolev, S.K., V. Ya. Tomashpolsky, A. O. Golosov, Some problems on second order curves with parameter, Current Problems of Teaching Mathematics at Technical University, (10), 92-97, ISSN 2307-5430, 2023, DOI: 10.25206/2307-5430-2023-10-92-97.
4. Modenov, P., А. Parchomenko, Sbornik zadach po analiticheskoy geometrii, Nauka, Moska, 1976.

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