IKKINCHI TARTIBLI CHIZIQLAR VA ULARNING XOSSALARI

Authors

  • Jalolxon Nuritdinov Tursunboy o‘g‘li Qo‘qon Davlat Pedagogika Instituti o‘qituvchisi Tel: +99895081816. E-mail: nuritdinovjt@gmail.com Author
  • Abdujalilova Maxliyo Abduvoxid qizi Qo‘qon Davlat Pedagogika Instituti talabasi Author

Keywords:

Ellips, giperbola, parabola, asimptotik yo‘nalishlar, optik xossalar.

Abstract

Bu maqolada ikkinchi tartibli chiziqlarning ta’riflari, turlari, umumiy va kanonik tenglamalari keltirilgan. Shuningdek ellips, giperbola va parabolalarni yasashning turli usullari yoritilgan. Ellips va parabolalarning optik xossalari geometrik usullar yordamida isbotlangan. Maqola so‘ngida ikkinchi tartibli chiziqlarning texnikaga tatbiqlari o‘rganilgan.

References

1. Apostol T.M. Calculus: Volume II, Multi-variable Calculus and Linear Algebra with Applications to Differential Equations and Probability. Wiley. 1991. 673p.

2. Narmanov A.Y. Analitik geometriya. Innovatsion rivojlantirish nashriyot-matbaa uyi, 2020 y, 160 bet.

3. Boyer C.B. and Merzbach U.C. A History of Mathematics. (3rd ed.). Wiley. 2011. 688p.

3. Александров П.С. Лекции по аналитической геометрии, пополненные необходимыми сведениями из алгебры с приложением собрания задач. Санкт-Петербург: Лань, 2022.–912с.

4. Gray A. Modern Differential Geometry of Curves and Surfaces with Mathematica (3rd ed.). CRC Press. 2006. 1016p.

5. Моденов П.С. Аналитическая геометрия. М. Изд-во МГУ, 1969.

6. Downs J.W. Practical Conic Sections: The Geometric Properties of Ellipses, Parabolas and Hyperbolas. Dover Publications. 2003. 100p.

7. Thomas L. H. Treatise on Conic Sections. Legare Street Press. 2022. 426p.

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Published

2025-01-26