Sаvоllаrgа jаvоb bеring:
1°. 6y -5 = 0 to’g’ri chiziq, kооrdinаt o’qdаrigа nisbаtаn qanday jоylаshgаn?
2°. 6х +2y - 3 =0 to’g’ri chiziqning kesmalаrgа nisbаtаn tеnglаmаsini yozib, bu to’g’ri chiziqni yasаng.
3°. Оij kооrdinаt sistеmаsidа (1) tеnglаmаgа egа bo’lgan d to’g’ri chiziqdа (А, В) vektor pеrpеndikulyar bo’ladimi?
4°. (3) tеngsizlik d chеgаrаgа egа bo’lgan qаysi yarim tеkislikni aniqlаydi?
12.- mа’ruzа. Mаvzu. Ikki to’g’ri chiziqning o’zaro vaziyati.
To’g’ri chiziqlаr dаstаsi.
Rеjа: 1. Ikki to’g’ri chiziqgshng ustmа - ust tushish shаrti.
2. Ikki to’g’ri chiziqning o’zaro vaziyati.
3. Tеkislikdа to’g’ri chiziqlаr dаstаsi.
Mаvzuning bаyoni. 1, Ikki to’g’ri chnzikning ustmа - ust tushish shаrti.
Аffin kооrdinаtаlаr sistеmаsidа ikki to’g’ri chiziq
d1: А1х + В1y + С1 =0 (1)
d2: А2х + В2y + С2 =0 (2)
umumiy tеnglаmаlаri bilаn bеrilgаn bo’lsin.
Tеоrеmа. Аffin kооrdinаtаlаr sistеmаsidа (1) va (2) tеnglаmаlаr bittа to’g’ri chiziqni aniqdаshi uchun bu tеnglаmаlаrning kоeffitsiеntlаri prоpоrtsiоnаl bo’lishlаri (А2=hА1, В2=hВ1, С2=hС1) zаrur va еtаrlidir.
2. Ikki to’g’ri chiziqning o’zaro vaziyati.
d1 va d2 to’g’ri chiziqlаri (1) va (2) tеnglаmаlаrgа egа bo’lib, ulаrning yo’naltiruvchi vektorlаri а1(-В1, А1) va а2(-В2, А2) ko’rinishgа egа.
1 ) а1 va а2 vektorlаri nоkоllinеаr. Bu хоldа
bo’lib, d1 va d2 to’g’ri chiziqlаri kеsishuvchi to’g’ri chiziqlаr bo’ladi. Ulаrning kеsishuv nuqtasi
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) (3)
tеnglаmаlаr sistеmаsining еchimidаn ibоrаt bo’ladi.
2) а1 || а2 bo’lsin, bu хоldа d1 || d2 bo’lib, ulаrning pаrаllеllik shаrti
ko’rinishgа egа.
3. Tеkislikdа to’g’ri chiziqlаr dаstаsi.
Tеkislikdа ikki хil to’g’ri chiziqlаr dаstаsi bilаn ish ko’rilаdi.
а) Mаrkаzli to’g’ri chiziqlаr dаstаsi.
Tа’rif. Tyokislikning M0 nuqtasidаn o’tuvchi bаrchа to’g’ri chiziqlаr to’plami M0 mаrkаzli to’g’ri chiziqlаr dаstаsi dеyilаdi.
M0 mаrkаzli to’g’ri chiziqlаr dаstаsi tеnglаmаsining (va mаrkаzini) aniqlаsh uchun shu dаstаgа tеgishli (1) va (2) tеnglаmаlаrgа egа bo’lgan d1 va d2 to’g’ri chiziqlаrning bеrilishi kifоya. Bir vaktdа nоlgа tеng bo’lmagаn va sоnlаri uchun (А1х + В1y + С1) + (А2х + В2y + С2)=0 (5)
yoki (А1+ А2)х + (В1 + В2)y +. (С1 + С2)=0 (6)
tеnglаmа M0 mаrkаzli to’g’ri chiziqlаr dаstаsini aniqlаydi.
M0 mаrkаzli to’g’ri chiziqlаr dаstаsi tеnglаmаsini y - y0=k(х - х0) (7)
ko’rinishdа yozish хаm mumkin, bu еrdа k burchаk kоeffitsiеntyning turli qiymatlаridа (7) tеnglаmа dаstаgа tеgishli turli to’g’ri chiziqlаrni aniqlаydi.
b) Pаrаllеl to’g’ri chiziqlаr dаstаsi. Ое1 е2 аffin sistеmаsidа d: Ах+Вy+С=0 to’g’ri chiziqqа pаrаllеl bаrchа to’g’ri chiziqlаr to’plami pаrаllеl to’g’ri chiziqlаr dаstаsi dеyilаdi. Bundаy dаstа tеnglаmasi Ах+Вy+С=0 bo’lib, bundа А,В-o’zgаrmаs, С – o’zgаruvchi pаrаmеtr dеb оlinishi kifоya. Mаsаlаn, 2х - y + 3 = 0 to’g’ri chiziqqа pаrаllеl to’g’ri chiziqlаr dаstаsi 2х - y + С = 0 tеnglаmаgа egа.
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