IKKINCHI TARTIBLI CHIZIQLARNING QUTB KOORDINATALARIDAGI TENGLAMALARI, ULARNING ANALITIK TAHLILI VA GEOMETRIK TALQINI
Ключевые слова:
konika, qutb koordinatalar, eksentrisitet, fokus, direktrisa, ellips, parabola, giperbola, analitik geometriya.Аннотация
Ushbu maqolada ikkinchi tartibli chiziqlarning (konikalar) qutb koordinatalardagi tenglamalari, ularning analitik tahlili va geometrik talqini o‘rganiladi. Natijalarda konikalarning umumiy tenglamasi ko‘rinishda ifodalanishi, bu yerda - eksentrisitet orqali ularning turlari aniqlanishi ko‘rsatildi. Muhokamada ushbu tenglamalarning mexanika, astronomiya va optikadagi qo‘llanilishi tahlil qilindi. Xulosa sifatida qutb koordinatalar konikalarni tabiiy va qulay ifodalash vositasi ekanligi asoslandi.
Библиографические ссылки
George B. Thomas – Calculus and Analytic Geometry
Thomas, G. B., Weir, M. D., & Hass, J. (2010). Thomas’ Calculus (13th ed.). Pearson Education.
Saparboyev J.Y. (2024). O‘quvchilarning amaliy faoliyatida fazoviy tasavvurini rivojlantirish mexanizmlari. Eurasian Journal of Academic Research, 7 (Special Issue), 631-633.
David Gilbert. Grundlagen der Geometrie (Geometriya asoslari). - Leipzig: Teubner, 1899.
Euclid. Elements. - Translated by T. L. Heath. - Cambridge: Cambridge University Press, 1908.
Greenberg, M. J. Euclidean and Non-Euclidean Geometries: Development and History. – 4th ed. – New York: W. H. Freeman, 2008.
Dilnoza, M. Use of the Acmelological Approach to Teaching Mathematics. International Journal of Innovative Analyses and Emerging Technology. c-ISSN, 2792-4025.
Abduraxmonova, R., & Mahmudova, D. (2025). Nuqtadan to'g'ri chiziqqacha bo'lgan masofa. Ikki to'g'ri chiziq orasidagi burchak. В theoretical aspects in the formation of pedagogical sciences (Т. 4, Выпуск 7, сс. 74–78). Zenodo. https://doi.org/10.5281/zenodo.15186643
Abdulhayeva, G., & Mahmudova, D. (2025). Tekislikda to'g'ri chiziq tenglamalari va ularni amaliyotga tadbiqi. В theoretical aspects in the formation of pedagogical sciences (Т. 4, Выпуск 7, сс. 35–40).
Karimberdiyeva , D. ., & Mahmudova , D. . (2025). Tekislikdagi perspektiv-affin moslikning o’ziga xos xususiyatlari. Развитие педагогических технологий в современных науках, 4(3), 114–117.
Maxmudova, D. X. (2023). Kognitiv kompetentlikni rivojlantirishning akmeologik texnologiyasini joriy etish shart-sharoitlari. GOLDEN BRAIN, 1(34), 19-24.
Ismoilova, D., & Mahmudova, D. (2025). Ko ‘po ‘lchovli yevklid fazosi: o ‘qitish texnologiyasi asosida yondashuv. In Innov. Conf. Published online April (Vol. 17, No. 2025, pp. 1-7).
Khaitmirzayevna, Makhmudova D. "Pedagogical Ways of Cognitive Competences in Future Teachers Based on Acmeological Approach." World Economics and Finance Bulletin, vol. 32, 23 Mar. 2024, pp. 146-148
Abdiqayumov, A., & Maxmudova, D. (2025). Central and parallel projections and their properties. Теоретические аспекты становления педагогических наук, 4(8), 177-184.
Abdulhamidova, M., Maxmudova, D. Proyektiv geometriyaning asosiy faktlari. (2026). Zamonaviy taraqqiyot va fan: 21-asr yondashuvlari, 6(1), 282-293. https://journalss.org/index.php/zam/article/view/25424
Загрузки
Опубликован
Выпуск
Раздел
Как цитировать
