to’g’ri chiziqning boshqa turdagi tenglamalari

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1662926504.doc ( ) 0 0 0 , y x m } { n m a , = r ( ) y x m , а r м м 0 n y y m x x 0 0 - = - t mt x x = - 0 nt y y = - 0 î í ì + = + = , , 0 0 nt y y mt x x ( ) ( ) 2 2 2 1 1 1 , , , y x m y x m 2 1 m m a = r 1 2 1 1 2 1 y y y y x x x x - - = - - х y d o m a n n r d п r a п r х } { a a sin cos n , 0 = r 1 0 = п r ( ) y …

2 5 = + + y x n r х y ( o m ( n � embed equation.3 �� _1077283716.unknown to’ђri chiziqning boshqa turdagi tenglamalari to’g’ri chiziqning boshqa turdagi tenglamalari reja: 1. ikki to’гri chiziq orasidagi burchak 2. ikki to’гri chiziq tenglamasini birgalikda tekshirish. 3. nuqtadan berilgan to’гri chiziqgacha bo’lgan masofa. agar to’гri chiziqning berilgan nuqtasi va uning yo’naltiruvchi vektori bo’lsa, uning tenglamasini quyidagicha tuzsa хam bo’ladi. faraz qilaylik, nuqta to’гri chiziqning ¢zgaruvchi nuqtasi bo’lsin. u holda, va vektorlar o’zaro parallel bo’ladi. vektorlarning kolleniarlik shartiga ko’ra (8) bu tenglama to’гri chiziqning kanonik tenglamasi deb ataladi. agar (8) da kasrlarni ga tenglasak, , yoki parametrik tenglamalar deb ataluvchi tenglamani hosil qilamiz. agar to’гri chiziqning ikkita nuqta- lari ma’lum bo’lsa, u holda vektorni yo’naltiruvchi vektor deb qarash mumkin, shuning uchun bu to’гri chiziqning tenglamasi (8) ga ko’ra (9) bo’ladi. bu tenglama ikki nuqtadan o’tgan to’гri chiziqning tenglamasi deb ataladi. 2-rasm. endi, …

i. to’гri chiziqga doir turli masalalar. 1. ikki to’гri chiziq orasidagi burchak. faraz qilaylik, bizga va to’гri chiziqlar berilgan bo’lsin. ma’lumki, bu erda lar mos ravishda to’гri chiziqlarning o’qiga oгish burchaklaridir. bu burchaklarni tekisligidagi musbat yo’nalish bo’ylab хisoblangan deb tushunamiz. agar > bo’lsa , to’гri chiziqlar orasidagi burchak deb burchakni tushunamiz. u holda (12) (12) dan ko’rinadiki, agar bo’lsa, yoki bo’ladi, ya’ni va to’гri chiziqlar parallel bo’ladi, va aksincha, agar va to’гri chiziqlar parallel bo’lsa, , bundan esa kelib chiqadi. shu sababli, tenglik to’гri chiziqlarning parallellik sharti deb ataladi. agar va to’гri chiziqlar perpendikulyar, ya’ni bo’lsa, u holda (12) dan munosabat kelib chiqadi. bu tenglikni to’гri chiziqlarning perpendikulyarlik sharti deb ataymiz. 2. ikki to’гri chiziq tenglamasini birgalikda tekshirish. faraz qilaylik , bizga ikki va to’гri chiziqlarning tenglamalaridan tuzilgan (13) sistema berilgan bo’lsin. ma’lumki, bu sistema yagona echimga ega bo’lishi uchun bo’lishi zarur va etarlidir. bu esa tengsizlikka ekvivalent. bu holda …

chiqadi. demak, nuqtadan berilgan to’гri chiziqgacha bo’lgan masofani topish uchun, nuqtaning koordinatalarini to’гri chiziqning normal tenglamasini chap tomonidagi noma’lumlar o’rniga qo’yish kifoya ekan. agar to’гri chiziq tenglamasi normal bo’lmasa, u holda normallovchi ko’paytuvchi yordamida normal ko’rinishga keltirib, so’ngra (15) formula yordamida talab qilingan masofani hisoblaymiz. to’гri chiziqlar dastasining tenglamasi. tekislikning nuqtasidan o’tgan barcha to’гri chiziqlari to’plami markazli to’гri chiziqlar dastasi deb ataladi. teorema . agar va lar nuqtada kesishuvchi to’гri chiziqlar, va lar bir vaqtda nolga teng bo’lmagan iхtiyoriy sonlar bo’lsa, u holda (16) nuqtadan o’tuvchi to’гri chiziq tenglamasi bo’ladi. isboti. avval (16) haqiqatan tenglama ekanligini ko’rsataylik, buning uchun uni quyidagi ko’rinishda yozib olamiz: (17) bu erda va lar bir vaqtda nolga teng bo’laolmaydi, chunki aks holda, embed equation.3 va embed equation.3 dan kelib chiqadi, buni esa bo’lishi mumkin emas, chunki bu to’гri chiziqlar shartga ko’ra kesishadi. bu esa (17) tenglama ekanligini ko’rsatadi. demak, u tekislikda biror to’гri chiziqni ifodalaydi. …

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1662926504.doc ( ) 0 0 0 , y x m } { n m a , = r ( ) y x m , а r м м 0 n y y m x x 0 0 - = - t mt x x = - 0 nt y y = - 0 î í ì + = + = , , 0 0 nt y y mt x x ( ) ( ) 2 2 2 1 1 1 , , , y x m y x m 2 1 m m a = r 1 2 1 1 2 1 y y y y x x x x - - = - - х y d o m …

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