I bob Oliy algebra va geometriya elementlari. 1-§ Tenglamalar sistemasini Kramer va Matritsa usuli bilan yechish
-§ Vektorlar yordamida hajmni hisoblash
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1-LHI, IAQ-1 (2)
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- 9-§ Ikkinchi tartibli egri chiziqlar
8-§ Vektorlar yordamida hajmni hisoblash Uchlari A1, A2, A3, A4 nuqtalarda bo‘lgan piramida hajmi topilsin. Uning A4 uchidan A1A2A3 yon yog’iga tushirilgan balandlik hisoblansin. 1. A1(4,-1,3), A2(-2,1,0), A3(0,-5,1), A4(3,2,-6) 2. A1(-1,2,-3), A2(4,-1,0), A3(2,1,-2), A4(3,4,5) 3. A1(-3,4,-7), A2(1,5,-4), A3(-5,-2,0), A4(2,5,4) 4. A1(1,1,-1), A2(2,3,1), A3(3,2,1), A4(5,9,-8) 5. A1(2,3,1), A2(4,1,-2), A3(6,3,7), A4(7,5,-3) 6. A1(1,1,2), A2(-1,1,3), A3(2,-2,4), A4(-1,0,-2) 7. A1(2,-1,2), A2(1,2,-1), A3(3,2,1), A4(-4,2,5) 8. A1(1,2,0), A2(3,0,-3), A3(5,2,6), A4(8,4,-9) 9. A1(-2,0,-4), A2(-1,7,1), A3(4,-8,-4), A4(1,-4,6) 10. A1(2,-1,-2), A2(1,2,1), A3(5,0,-6), A4(-10,9,-7) 11. A1(5,2,0), A2(2,5,0), A3(1,2,4), A4(-1,1,1) 12. A1(0,-1,-1), A2(-2,3,5), A3(1,-5,-9), A4(-1,-6,3) 13. A1(-1,-5,2), A2(-6,0,-3), A3(3,6,-3), A4(-10,6,7) 14. A1(2,1,4), A2(-1,5,-2), A3(-7,-3,2), A4(-6,-3,6) 15. A1(7,2,4), A2(7,-1,-2), A3(3,3,1), A4(-4,2,1) 16. A1(-4,2,6), A2(2,-3,0), A3(-10,5,8), A4(-5,2,-4) 17. A1(1,3,6), A2(2,2,1), A3(-1,0,1), A4(-4,6,-3) 18. A1(1,5,-7), A2(-3,6,3), A3(-2,7,3), A4(-4,8,-12) 19. A1(1,-1,1), A2(-2,0,3), A3(2,1,-1), A4(2,-2,-4) 20. A1(1,2,0), A2(1,-1,2), A3(0,1,-1), A4(-3,0,1) 21. A1(2,-4,-3), A2(5,-6,0), A3(-1,3,-3), A4(-10,-8,7) 22. A1(1,-1,2), A2(2,1,2), A3(1,1,4), A4(6,-3,8) 23. A1(-3,-5,6), A2(2,1,-4), A3(0,-3,-1), A4(-5,2,-8) 24. A1(-2,-1,-1), A2(0,3,2), A3(3,1,-4), A4(-4,7,3) 25. A1(0,-3,1), A2(-4,1,2), A3(2,-1,5), A4(3,1,-4) 26. A1(14,4,5), A2(-5,-3,2), A3(-2,-6,-3), A4(-2,2,-1) 27. A1(1,0,2), A2(1,2,-1), A3(2-2,1), A4(2,1,0) 28. A1(1,2,-3), A2(1,0,1), A3(-2,-1,6), A4(0,-5,-4) 29. A1(3,10,-1), A2(-2,3,-5), A3(-6,0,-3), A4(1,-1,2) 30. A1(-1,2,4), A2(-1,-2,-4), A3(3,0,-1), A4(7,-3,1) 9-§ Ikkinchi tartibli egri chiziqlar I. Quyidagi ikkinchi tartibli chiziqlarning turini aniqlab, fokusi, direktrisasi va asimptotalarini toping, uning grafigini yasang. 1. 16x2+4y-16=0 2. 9x2-16y2-144=0 3. 4x2+16y2-16=0 4. x2-2x+y2=0 5. x2-4x+y2=0 6. 2x-y2+4=0 7. 9x2+25y2-225=0 8. +1 9. 10. 11. x2-4x+y2+3=0 12. x2+y2-2y=0 13. x2-2x+1+y2-2y=0 14. y2+4y=x 15. 3x+y2=9 16. x2+3y=9 17. x2=y+2 18. x2-4y2+8x-24y=24 19. x2-4y2=16 20. 9x2-25y2=225 21. x2+y2-6y-9=0 22. x2+y2+x+y=0 23. x2+4y2-6x+8y=3 24. 25. 26. 9x2+16y2=144 27. 9x2-36y2=324 28. 4y=4x-x2 29. y2=6x-6 30. y2=x+1 II. 1) aylana A(1;-2), B(0;-1) va C(-3;0) nuqtalardan o‘tadi.Uning kanonik tenglamasi tuzilsin va grafigi yasalsin. Javob:(x+3)2+(y+5)2=25; 2) diametri A(-3;0), B(3;6),AB kesmadan iborat bo‘lgan aylana tenglamasi tuzilsin. Javob:x2+y2-6y-9=0; 3) 0(0;0) nuqtadan va berilgan x+y+1=0 to‘g’ri chiziq bilan x2+y2=1 aylananing kesishish nuqtalaridan o‘tuvchi aylana tenglamasi tuzilsin. Javob:x2+y2+x+y=0; 4) ellips ekstsentrisiteti = ga va kichik yarim o‘qi 3 ga teng bo‘lsa, uning kanonik tenglamasi tuzilsin. Javob:; 5) ellips fokuslarining biridan katta o‘qining uchlariga bo‘lgan masofalar 1 va 7 birlikka teng. Shu ellips tenglamasi tuzilsin. Javob:; 6) ellips bilan umumiy fokuslarga ega bo‘lgan va ekstsentrisiteti E= bo‘lgan giperbola kanonik tenglamasi tuzilsin. Javob:; 7) giperbola fokusidan asimptotalarigacha bo‘lgan masofa hisoblansin. Javob:5 birlik; 8) aylana x2+y2-4x-6y=0 markazidan A(-1;0) nuqtagacha bo‘lgan masofa topilsin. Javob:; 9) absissa o‘qiga 0(0:0) nuqtada urinuvchi va ordinata o’qini A(0;4) nuqtada kesuvchi aylana tenglamasi tuzilsin. Javob:x2+y2-4y=0; 10) A(4;6) nuqta berilgan. Diametri OA kesmaga teng bo‘lgan aylana tenglamasi tuzilsin. Javob: x2+y2-4x-6y=0; 11) x2+y2-4x+6y-5=0 aylananing absissa o‘qi bilan kesishadigan nuqtalaridan o‘tuvchi radiuslari orasidagi burchak topilsin. Javob: =900; 12) ellipsga ichki chizilgan kvadrat tomonining uzunligi topilsin. Javob:; 13) agar ellipsning fokuslari orasidagi masofa uning katta va kichik o‘qlari uchlarining orasidagi masofaga teng bo‘lsa, uning ekssentrisiteti toping. Javob:; 14) M(-1:2) nuqtadan o‘tib, koordinata o‘qlariga urinuvchi aylana tenglamasi tuzilsin. Javob: x2+2x+y2-2y+1=0 , x2+10x+y2-10y+25=0; 15) ellipsning tenglamasi 25x2+169y2=4225 ko‘rinishida bo‘lsa ,uning ekssentrisiteti topilsin. Javob: ; 16) ellipsda uning kichik o‘qidan 5 birlik masofada yotuvchi nuqta topilsin. Javob:(, ya’ni bunday nuqtalar to‘rtta; 17) ellips o‘qlarining nisbati ga teng. Shu ellips ekssentrisiteti topilsin. Javob: 0.8; 18) ellipsda shunday nuqta topilsinki, uning o‘ng fokusidan masofasi chap fokusigacha bo‘lgan masofasiga nisbatan 4 marta katta bo‘lsin. Javob: A(- va B; 19) ellipsda fokal radius-vektorlarining ko‘paytmasi kichik yarim o‘qning kvadratiga teng bo‘lgan nuqta topilsin. Javob: M1(3;0), M2(-3;0); Download 455.21 Kb. Do'stlaringiz bilan baham: |
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