III BOB. Analitik geometriya
1-§. To`g`ri chiziqning umumiy, vektor va kanonik tеnglamasi. To`g`ri chiziqning kеsmalar bo`yicha tеnglamasi. To`g`ri chiziqning burchak koeffitsiyentli tеnglamasi.
To’g’ri chiziq va uning tenglamalari.
To’g’ri chiziq tushunchasi analitik geometriyaning asosiy tushunchalaridan biridir. Quyida har xil holatlarda to’g’ri chiziqning analitik ifodalarini (tenglamalarini) keltirib chiqaramiz va ular yordamida to’g’ri chiziqning tekislikdagi vaziyatlarini o’rganamiz.
1) To’g’ri chiziqning burchak koeffitsientli tenglamasi. To’g’ri chiziqning
![](data:image/png;base64,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)
o’qi musbat yo’nalishi
bilan hosil qilgan burchagi ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAPCAIAAABiEdh4AAABHElEQVR4nGP5//8/AymAhSTV1NAAdOHixYunTZt29epVCwuL9evXAwUNDAxiYmIaGhrQNfz+/TspKengwYPLli3T1taOiIjYuXPnjh07ZGRkamtrsdiQkZGxcuXK48ePGxsbA7l+fn6rVq3av3//hQsXmJmZ0TUARRcsWJCSkgJRDQTv379fvXr11q1bpaSksPiht7cX6AGgJXDnbd68uaSkxNPTE7ungS5hZWUF+g/I/vPnT2xs7OnTp6dMmfL27dsfP35IS0ujaxASErp37965c+fY2NiAXvz7929AQMDRo0cXLlzY19eHxYapU6emp6fb2toCwwToE6BjZs+e3dLSsmTJEqARWDSYmpoCjUd2bjoYMKAC+icNggAAo1p9UBP8HpEAAAAASUVORK5CYII=)
va to’g’ri chiziqning ordinatlar o’qidan ajratgan kesmasining kattaligi berilganda, uning tekislikdagi holati aniq bo’ladi. Masalan,
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
bo’lsa, uning holati aniq bo’ladi (4-chizma).
![](data:image/png;base64,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)
y
y
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3
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b
3-chizma 4-chizma 5-chizma
Yuqoridagi miqdorlar berilganda to’g’ri chiziqning tenglamasini keltirib chiqaramiz.
![](data:image/png;base64,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)
to’g’ri chiziqqa tegishli ixtiyoriy nuqta bo’lsin (5-chizma).
![](data:image/png;base64,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)
to’g’ri
burchakli uchburchakdan ![](data:image/png;base64,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)
, bundan
5–chizmadan
![](data:image/png;base64,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)
; yoki
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
bo’lganligi uchun
![](data:image/png;base64,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)
bo’ladi.
![](data:image/png;base64,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)
to’g’ri chiziqning
burchak koeffitsienti deyiladi va
![](data:image/png;base64,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)
bilan belgilaymiz.
Shunday qilib,
![](data:image/png;base64,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)
(1) munosabat kelib chiqadi. Bunga to’g’ri chiziqning
burchak koeffitsientli tenglamasi deyiladi.
![](data:image/png;base64,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)
bo’lsa, to’g’ri chiziq koordinatlar boshidan o’tib, tenglamasi
![](data:image/png;base64,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)
bo’ladi.
![](data:image/png;base64,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)
bo’lsa,
![](data:image/png;base64,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)
bo’lib, bu birinchi koordinatlar burchagining bissektrisasi bo’ladi.
Do'stlaringiz bilan baham: