Geometriyadan misol va masalalar

a + b + c vektorning modulini aniqlang.


A) 12 B) 10

46. 
    Determinantni hisoblang.
    

A) 3 B) 4

46. 
    Determinantni hisoblang.
    

A)17 B) 14

46. 
    Determinantni hisoblang.
    

A) 92 B)100

46. 
    Determinantni hisoblang.
    

A)51 B) 207

100. 
     9 D)11
     

*5

42 4/125

C)-3 D)2

3. 
   %⁺¹=1
   

-4 -21

C) 15 D)-17

4 -3 5

3-2 8

1 -7 -5

C)-87 D)102

4 -3 5 1

3 -2 8 3

8 -6 10 2

1 -5 4 3

C)-43 D) 0

50. 
    Quyidagi chiziqli tenglamalar sistemasini Kramer usulida yeching.
    í3y - X = -17
    ^5% + 3y = -5
    

A)(5;-2) B)(2;-5) C)(-2;5) D)(-5;2)

50. 
    Quyidagi chiziqli tenglamalar sistemasini Kramer usulida yeching.
    

248

'^x + y + ^4 z = 1 < 2 x + y + 6 z = 2 3x + 3 y + 13z = 2 A)(-3; 2; 1) B)(2;3;-1) C)(1;2;3) D)(3;2;-1) a va ¿> vektorlar o‘zaro ^ = ■y burchak hosil qiladi. |cz| = 1, r.^-12 ¡¿>| = 2 ni bilgan holda, quyidagini hisoblang: [a ¿>] . A) 3 B) 4 C) 9 D) 2 a(3; -1; -2) va ¿>(1; 2; -1) vektorlar berilgan. Vektor ko‘paytmalar koordinatasini toping: [a ¿>]. A)(5;-1;7) B)(-3; 1;-7) C)(5; 1;-4) D)(5; 1; 7) a(3; -1; -2) va ¿>(1; 2; -1) vektorlar berilgan. Vektor ko‘paytmaning koordinatasini toping: [(2 a + ¿>)b]. A)(5;1;6) B)(10; 2; 14) C)(2; 5; 3) D)(4; 1; 5) 55. X(2; -1; 2), B(1; 2; -1) va C(3; 2; 1) nuqtalar berilgan. Vektor ko‘paytmaning koordinatasini toping: [ABBC]. A)(8; 2; -4) B)(5; 3; 12) C)(6; -4; -6) D)(3; -2; 5) 56. X(2; -1; 2), B(1; 2; -1) va C(3; 2; 1) nuqtalar berilgan. Vektor ko‘paytmalar koordinatalarini toping: [(BC - 2CA)CB]. A)(12; -8; 12) B)(10; 4; -6) C)(-11; 6; 4) D)(-12; 8; 12) 57. a(2; -2; 1) va ¿>(2; 3; 6) vektorlar orasidagi burchak sinusini hisoblang. ^5^17 A) sina = ^7 21 ... . 5V17 C) sina = 21

DA ■ ^3^17 B) sina = 21 TAI ■ 4^17 D) sina = ^7 21

58. X(3; -2; 5), B(1; 4; -3) va C(-6; 2; 4) nuqtalar berilgan bo‘lsa, [BC AC]AB aralash ko‘paytmasini toping. A) -13 B) -28

C)0 D)28

59. C(-2; 4; 3), 0(1; -5; 6) va E(3; 7; -4) nuqtalar berilgan bo‘lsa, (2CD - 3DE)(DC + 3CE)(2CD - ED) aralash ko‘paytmasini toping.


249



A) -3 B) 0 C) 3 D)-2

60. 
    a = i + 6j-4k, b = -3t + 2j + 7k va c = -5t-6j + 2k vektorlar berilgan bo‘lsa, [a c]b aralash ko‘paytmasini toping.
    

A) 240 B) 244 C) -240 D)120

60. 
    a = t + 6j-4k, b = -3t + 2j + 7k va c = -5t-6j + 2k vektorlar berilgan bo‘lsa, (b + 2a)(C + 3b)(2a - c) aralash ko‘paytmasini toping.
    

A) -920 B) 940 C) 960 D)-930

60. 
    a(6; -4; 8) va b(-2; 4; 0) vektorlar berilgan bo‘lsa:
    

^a+^b(b-1) topilsin.

A)(24; 12; -12) B)(-14; 13; 12)

C)(12; 24; -12) D)(-24; -12; 12)

60. 
    a (8; 4; 1) va b(2; -2; 1) vektorlardan yasalgan parallelogramm
    

yuzi hisoblansin.

A) 8V3 B) 18V2 C)18V3 D)9V2

60. 
    Berilganlarga ko‘ra a, b va c vektorlarning aralash ko‘paytmasini toping. a = k, b = t, c = j.
    

A) 1 B) -1 C) 0 D)-2

60. 
    a, b va c vektorlarning aralash ko‘paytmasini toping.
    

a = t+j, b = t - j, c = k.

A) 1 B) -1 C) 0 D)-2

60. 
    a va b vektorlar o‘zaro ^ = “ burchak tashkil qiladi va C vektor bilan perpendikulyar. |a| = 6, |b| = 3 va |c| = 4 berilgan bo‘lsa, abc ni toping.
    

A) 20 B) 36 C)-12 D) 24

60. 
    a = 2t + 3j + 4k, b = 3t + 2j + k va c=j-k vektorlar berilgan bo‘lsa, ([ac] b) ni toping.
    

A) -15 B) 12 C) 15 D) 10


250

60. 
    a = 2t + 3j + 4k, b = 3t + 2j + k va c=j — k vektorlar berilgan bo‘lsa, [(a — 2c)(3b — 2a)] ni toping.
    

A)(5; —40; 5) B)(40; 15; —5)

C)(—5; 40; —5) D)(—15; 45; 5)

60. 
    a = — i + 3j + k b = j + 2k va c = 2a — 3b vektorlar berilgan bo‘lsa, a[bc] c ni toping.
    

A)—146 B) —156 C) 180 D) —180

60. 
    a = — i + 3j + k, b = j + 2k va c = 2a — 3b vektorlar berilgan bo‘lsa, [a[ac]] b[ac] ni toping.
    

A)1926 B) 1350 C) 2120 D)2020

60. 
    Quyida berilgan aylana tenglamasidan aylana markazi va radiusi topilsin.
    

X² + y² — 6y = 0

1. 
   R = 3, (0; 3); C) R = 9, (0;3);
   
2. 
   R = 3, (0; —3); D) R = 9, (0; —3).
   

60. 
    Ellipsning yarim o‘qlarini toping: “ + ^ = 1.
    

A) ±3 va ±5 C) 3 va 5

B) ±5 va ±3 D) 5 va 3

60. 
    Quyidagilardan qaysi biri ellips tenglamasini ifodalaydi?
    

1. 
   x² + 25y² =4 C) x² — 16y² = 16
   
2. 
   x² + 9y² = 0 D) x² — y² = 1
   

60. 
    Radiusi R = 5, markazi (2; —4) nuqtada bo‘lgan aylana tenglamasini toping.
    

1. 
   x² + y² + 4x + 8y + 5 = 0
   

3. 
   x² + y² — 4x — 8y + 5 = 0
   

2. 
   x² + y² + 4x — 8y — 5 = 0
   

4. 
   x² + y² — 4x + 8y — 5 = 0
   

60. 
    Ellips fokuslarining koordinatalarini toping: + = 1.
    

A) (±6; 0) C) (6; 0) B) (0;±6) D) (0;—6)


251

60. 
    Quyidagi ellips tenglamasining ekssentrisitetini aniqlang: x² + 4y² = 1
    

B) e = ±V3


77. Direktrisalari


3

3. 
   e = —
   

2

V3

4. 
   ^£ = ±^ 2
   

x = ± - ekssentrisiteti e = bo‘lgan ellips

100. 
     3.v² + 7y² = 1
     

4. 
   3.v² + 7y² = 21
   

tenglamasining fokuslari orasidagi masofani


tenglamasi topilsin.

1. 
   7x² + 3y² = 21
   
2. 
   7x² + 3y² = 1
   

78. 
    Quyidagi ellips
    

aniqlang: — + — = 1
25 169

A) 8 B) 12 C)18 D) 24

78. 
    Yarim o‘qlari 2 va 5 bo‘lgan ellips tenglamasini ko‘rsating.
    

1. 
   i2 + ^2=1 C) - + ⁷² = 1
   

⁷ 4 25 ⁷ 2 5

2. 
   - + ⁷² = 1 d) - + ⁷² = 1
   

⁷ 5 2 ⁷ 25 4

78. 
    Tekislikda berilgan nuqtadan bir xil uzoqlikdagi nuqtalarning
    

geometrik o‘rniga deyiladi.

1. 
   ellips C) shar
   
2. 
   aylana D) giperbola
   

78. 
    Parabola tenglamasining umumiy ko‘rinishini ko‘rsating.
    

1. 
   ^ + 72=1 C) y² = 2px
   

a² b²

2. 
   A'² + y² = R² D) 22 - ⁷² = 1
   

a² b²

78. 
    y² = 8% parabolaning direktrisasini toping.
    

A) y = 2 C) x = 2


B) y = -2 D) x = -2

78. 
    Direktrisasi y = —6 bo‘lgan parabola tenglamasini aniqlang.
    

1. 
   y² = 24% C) y² = —24%
   
2. 
   x² = 24y D) x² = —24y
   

78. 
    y² = 12% parabola tenglamasining fokusi nimaga teng?
    

252

1. 
   F(0; 3) C) F(3; 0)
   
2. 
   F(0; -3) D) F(-3;0)
   

78. 
    Agar F(-5; 0) fokus va direktrisa Otenglamasi x = 5 bo‘lsa, parabola tenglamasini tuzing.
    

1. 
   y² = -20% C) y² = -10%
   
2. 
   y² = 20% D) y² = 10%
   

78. 
    Quyidagi nuqtalardan qaysilari y² = 18% parabolaga tegishli?
    

1. 
   A(2; 6) C) C(1; 18)
   
2. 
   B(2; 36) D) D(-1;18)
   

78. 
    Ushbu nuqtalar tegishli bo‘lgan parabola tenglamasi toping?
    

A(-7; 7),B(-1;V7).

1. 
   y² = -6% + 7 C) y² = -2% + 5
   
2. 
   y² = -7% D) y² = -V7x
   

78. 
    Parabolaning fokusidan direktrisasigacha bo‘lgan masofa 4 ga teng.
    

Uning kanonik tenglamasini tuzing.

1. 
   y² = 16% C) y² = -8%
   
2. 
   y² = -16% D) y² = 8x
   

78. 
    y² = 20% parabola tenglamasi berilgan. Fokal radiusi 10 ga teng bo‘ladigan M nuqtani toping.
    

1. 
   (8; -11), (8; 11) C) (11; -8), (11; 8)
   
2. 
   (-11; 8), (11; 8) D) (-8; 11), (8; 11)
   

78. 
    x² = 10y parabola (5; 7) nuqtadan o‘tganda ushbu nuqtada fokal radius topilsin.
    

1. 
   V4Ï C) V26
   
2. 
   V53 D) V50
   

78. 
    Giperbola tenglamasi uchun qaysi shart bajarilganda teng yonli giperbola deyiladi?
    

1. 
   а Ф b C) a > b
   
2. 
   а < b D) а = b
   

78. 
    Haqiqiy o‘qi 10, mavhum o‘qi 8 ga teng bo‘lgan giperbola tenglamasi topilsin.
    

253

Í2 - 2Ï = 1 ^7 64 100 ^1

^x— - ^y— = 1 ^7 10 8 - ^y2 = 1

93.Fokuslari orasidagi masofa 2c = 8, ekssentrisiteti c = 4 bo‘lgan giperbolaning kanonik tenglamasini aniqlang. у - ^y2 = 1 ^2 - ^y2=1 94 £2-^=1 a^2 b^2

— - ^ = 1 ^7 7 9 ^2 + ^y2 = 1 giperbolaning ixtiyoriy nuqtasidan uning ikki

asimptotasigacha bo‘lgan masofalar ko‘paytmasi har doim ga teng bo‘ladi. ab о , о a^2+b^2a^2b^2 — a+b

C) a^2+b^2 — a+b

95. ^-^=1 giperbola tenglamasi berilgan bo‘lsa, uning yarim o‘qlari topilsin. 3 va 8 8 va 3 96. Yarim o‘qlari nimaga teng?

-8 va -3 -3 va -8 a = 6, b = 4 bo‘lgan giperbolaning ekssentrisiteti

A) 4|3 B)-4|3 C) -4|3 D) 4|3 97. ~ -^ = 1 giperbolaning asimptotalarini aniqlang. ^y = ±Jü^x ^x = JI^y

у = ±^х