Geometriyadan misol va masalalar

х = ±^У


98. Asimptotalari у = ±4x , fokuslari orasidagi masofa 20 bo‘lgan giperbolaning ekssentrisitetini toping.

5 5 4 3

A) _E = - B) _£ = - C) c = - D) _£ = -


254

99. 
    Quyidagi nuqtalardan qaysi biri ushbu giperbolani qanoatlantiradi:
    

*² _ y² _ i

20 14 ^—

1. 
   (2-/10 ; V14) C) (V10 ; V14)
   
2. 
   (2V10 ; 2V14) D) (V10 ; 2V14)
   

99. 
    Teng tomonli giperbola x² — y² = 18 berilgan. Unga fokusdosh
    

100. 
     ^x— — ^y2 = 1
     

⁷ 20 16

4. 
   f — ^ =1
   

o‘qiga nisbatan


simmetrik bo‘lgan B


C) B(4;f)
o‘qiga nisbatan


5^

C) C(2;f)

D) B(—4;^) simmetrik bo‘lgan C


D) C(2;^)


bo‘lib, M(10; 8) nuqtadan o‘tuvchi giperbolaning tenglamasi topilsin.

A) T2 — ^y2 = 1

b) |22—y²=1

101. 
     X(4;2^) nuqtaga qutb
     nuqtani toping.
     

2^ 5^

A) B( 4;-) B) B(4;^)

2re.

101. 
     B(2;—) nuqtaga qutb
     nuqtani toping.
     

A) C(2;|) B) C(—2;^)

103. 
     X(3;-) nuqtani qutb o‘qi atrofida — burchakka musbat
     

64

yo‘nalishda burilsa bu nuqtaning koordinatalarini aniqlang. 17^ 2^ 2^ 5^

A) (3;-7^) B) (3;^) C) (—3;^) D) (3;^)

103. 
     Qutb koordinatalar sistemasida X(8;— -^) va B(6;^) nuqtalar
     

berilgan. AB kesma o‘rtasining koordinatalarini toping.

2 77 77 2 77 2 77

* x z z-x 1 v X ■ x X z* z“v / v X z*~x x z* J v X ■ X x z* i w X

A) (3;—^) B) (2;-) C) (1;—) D) (1;-)

103. 
     Dekart koordinatalar sistemasida M(V3; 1) nuqta berilgan. Uni
     

qutb koordinatalarini toping.

^ 2^ ^

4 x z* 1 w X i x x z* Ad / v x x—•< x z* 1 w X

A) (2; 6) B) (1; -) C) (2; 3)

D) (3;|)

103. 
     Qutb koordinatalarida a radiusli, markazi koordinatalar boshida
     

bo‘lgan aylana tenglamasini toping.

A) r = 2a B) r = a C) r = a² D) r = 3a

255

103. 
     Qutb koordinatalar sistemasida M(3;—) va A(2;-) nuqtalar
     

6' 6'

orasidagi masofani toping.

A) V19 B) 2 C) 3 D)V5

2

103. 
     Qutb koordinatalar sistemasida r — ^_os tenglama bilan berilgan
     

chiziqni dekart koordinatalar sistemasida tenglamasini toping.

1. 
   y² — 4(x + 1)
   
2. 
   y² + x² — 1
   
3. 
   x — y²
   
4. 
   ^2 + ^—1
   

103. 
     Qutb koordinatalar sistemasida M(3;—) va A(4;-) nuqtalar
     

" ^v ’6' " 3'


orasidagi masofani toping.

A) 6 B) 3 C) 7 D) 5

103. 
     P — 411^^ parabolaning direktrisa tenglamasini toping.
     

A) x — 5 B) x — -3 C) x — -1 D) x — -2

103. 
     Quyidagi 3x² — 2xy + 3y² + 2x — 4y + 1 — 0 egri chiziqni markazi topilsin.
     

A) (—1;1) B) (-1;8) C) (1;-4) D) (2;-3)

103. 
     4xy + 3y² + 16% + 12y - 36 — 0 berilgan ikkinchi tartibli chiziqning turini aniqlang.
     

A)giperbola B)parabola C)parallel to‘g‘ri chiziqlar D)ellips

103. 
     Ushbu 9x² - 16y² - 54% - 64y - 127 — 0 ikkinchi tartibli chiziqning eksentrisitetini aniqlang.
     

3 4 5 7

^A) 4 ^B) 5 ^C) 4 ^D) 5

103. 
     Quyidagi 32x² + 52xy - 7y² + 180 — 0 egri chiziqning
     

asimptotalarini toping.

A) ±|x B) ±4% C) ±4% D) ±i*

103. 
     14x² + 24xy + 21y² - 4x + 18y - 139 — 0 ellipsning fokuslari orasidagi masofani aniqlang.
     

A) 5 B) 6 C) 10 D) 8


256

103. 
     Ushbu 7x² + 60xy + 32y² — 14% — 60y + 7 = 0 ikkinchi
     

tartibli chiziqning tipini aniqlang.

A) giperbola B) parallel to‘g‘ri chiziqlar C) ellips D) parabola

103. 
     Quyidagi 9x² + 24xy + 16y² — 230% + 110y — 475 = 0
     

tenglama bilan berilgan ikkikinchi tartibli chiziqning direktrisasini aniqlang.

A) X = — — B) X = — — C) X = — — D) X = — —

103. 
     Ushbu 5x² + 12xy — 12% — 22y — 19 = 0 egri chiziqning haqiqiy o‘qining burchak koeffitsiyentini aniqlang.
     

A) к =¹ B) к = ³ C) к = ² D) к =¹

103. 
     Quyidagi 5x² + 8xy + 5y² — 18% — 18y + 9 = 0 ikkinchi
     

tartibli chiziqning markazi qaysi nuqtada joylashgan?

A) (1;1) B) (—2; 3) C) (—3;1) D) (—1;1)

103. 
     6xy — 8y² + 12% — 26y — 11 = 0 tenglama bilan berilgan ikkinchi tartibli chiziqning turini aniqlang.
     

A) parabola B) ellips C) parallel to‘g‘ri chiziqlar D) giperbola.


257

SINOV TESTI JAVOBLARI №	0	1	2	3	4	5	6	7	8	9
0		С	D	C	A	B	D	A	A	A
1	A	C	B	A	D	C	C	D	C	B
2	D	A	D	B	A	C	B	B	C	A
3	A	C	B	A	B	C	A	A	B	A
4	B	C	B	D	A	B	A	C	B	D
5	B	D	A	D	B	C	D	A	C	B
6	A	C	D	B	A	D	B	A	C	D
7	B	A	C	A	D	B	C	D	B	A
8	B	C	D	B	C	A	A	B	D	C
9	A	D	B	B	C	A	D	C	B	A
10	C	B	D	A	C	A	B	A	A	D
11	C	B	A	C	A	C	B	D	C	A
12	D

258



JAVOBLAR

1. 
   1) 5; 2) Т34; 3) 13; 4) Т2. 1.2.2. 1) /137; 2) 5; 3) 11; 4) 1.
   

1.2.3. (2; 4). 1.2.4.(3; 3). 1.2.5.(—; б). 1.2.6. (0; -10). 1.2.7. (0; —).

^v ’ ^{7 v} ’ ⁷ \24 J \ 2 )

1.2.8. (-⁵;0). 1.2.9. (89; 0). 1.2.10. (5;3). 1.2.11. ЛВС uchburchak 3 к10

to‘g‘ri burchakli. 1.2.12. (-7;0) va (17; 0); (0;9-10Т2),

(0;9 + 10V2). 1.2.13. (0; 11 + 4Тб), (0; 11 - 4Тб). 1.2.14. 5.

1.2.15. (2; 2); (12; -12); (б; -б); (-4; 4). 1.2.16. М(-5; 4). 1.2.17. Markazi (-1; -2) nuqtada, radiusi г = 5 ga teng. 1.2.18. В(2; 5); D(16; 3). 1.2.19. M(2; 10). 1.2.20. M1(1; -1), г1 = 1; М₂(-5; -5), г₂ = 5. 1.2.21. М1(4 + Тб; 4 + Тб), г1 = 4 + Тб; М₂(4 - Тб; 4 - -Тб), г₂ = 4 - Тб. 1.2.22. 5. 1.2.23. /29. 1.2.24. 5 + 2Т10 + 5Т5. 1.2.25. (-5; 2). 1.2.27. (3; 5); (4; 2); (5; -1). 1.2.28. (4; -4); (2; 5).


1.2.29. 8. 1.2.30. 13. 1.3.1. (0; 2). 1.3.2. (1; -1). 1.3.3. (3; -3). 1.3.4.


(-2; 2). 1.3.5. (1;3). 1.3.6.(-1; 4); (0;0);

(0;-11). 1.3.8. X = 1 (х1 + х₂ + х₃);


(1;1). 1.3.7. (11; 0) va \2 2/ 5

У = ¹⁽У1 ⁺У2 ⁺Уз).

9. 
   (-3; 3); (7; 5); (-3;-3). 1.3.10. (4; 1); (1; 4); (4; 4). 1.3.11.
   

В(0;-7). 1.3.12. W(0;9). 1.3.13. В(12;-4). 1.3.14. С(10;9);


D(4;-4). 1.3.15. 4. 1.3.16. М(12;-11) 1.3.17. D(8;-18). 1.3.18.


С(0;-1); D(4;-4). 1.3.19. (0; у) ;


(-3;у). 1.3.20. 4(3;-1);


В(0;8). 1.3.21. 4(-5;3); В(4; 3). 1.3.22. В (-5;^). 1.3.23.


С(1;-4). 1.3.24. С(-9; 7). 1.3.25. 4(100;-131); В(-225; 184).