ข้อสอบ เรขาคณิตวิเคราะห์ พร้อมเฉลย pdf

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1. P(4, y) A(-5, 2) B(13, -6) y

2. A(2, 7) , B(-5, 6) A

34

A B

3. (k, 7) (-3, -2) (3, 2) (1, -4) k

4. (7, 5) x + 2y + 12 = 0

5. (2, 1) 2x + 3y = 3 3x 2y = 11

6. 5x + 12y 2 = 0 3

7. (-1, 2) 4x 3y 5 = 0

Pra Fun Math 2 --------------------------------------------------------------------------------------------------------------------------------------------------------- 8. (7, -3) x

9. x2 + y2 + 4x 2y + 1 = 0

10. k x2 + y2 8x + 10y + k 10 = 0 5

11. x2 + y2 4x 2y 20 = 0 (5, 5)

12. 12.1 x2 + 4x + 12y 8 = 0

12.2 y2 6y + 4x + 1 = 0

Pra Fun Math 3 ---------------------------------------------------------------------------------------------------------------------------------------------------------

13. y = 3 (0, -3)

14. (2, 1) x y (-1, -5) (-1, 7)

15. 25x2 + 9y2 100x + 18y 116 = 0

16. 4 2 x

17. P(x, y) (0, -3) (0, 3) 10

18. 2 22

10 5

x y = 1 13,

2

Pra Fun Math 4 ---------------------------------------------------------------------------------------------------------------------------------------------------------

19. y2 + 4x = 100

20. 16x2 9y2 64x 18y 89 = 0

21. 21.1 (5, 0) , (-5, 0) (0, -4)

21.2 (0, -1) , (0, 1) 15

y x

21.3 x = 1 8 (4, -2)

Pra Fun Math 5 ---------------------------------------------------------------------------------------------------------------------------------------------------------

PAT1

B PAT1 .. 51

1. C x 2y = 0 x2 = 8y C 2x y = 1

1. 5

6 2. 5

7 3. 7 4. 5

7

2. (1, 2) X 6 4 1. (0, 1) 2. (2, 0) 3. (1, 4) 4. (4, 1)

3. P(-1, -1) Q(1, c) XY l P, Q 3 -2 Q 1. y = -2x + 7 2. y = -2x + 5 3. y = -2x + 3 4. y = -2x + 1

4. 21,CC 8)2()1(2 22 yx 2C 1

2C )3,32(

1. 24)321( 22 yyx 2. 24)321( 22 yyx 3. 24)321( 22 yyx 4. 24)321( 22 yyx

PAT1 .. 52

5. 0442 xyy ),( ba ba

1. 4 2. 5 3. 6 4. 7

6. (2, 1) 1x 3

1

1. (0, 1) 2. (0, 2) 3. (1, 0) 4. (3, 0)

7. )0,3(

2

21,2

1. )0,4( 2. )2

25,0( 3. )0,6( 4. )23,0(

PAT1 .. 52

8. 1l 2l 20)5( 22 yx P Q

P Q 1l 052 yx 2l

1. )2

5,0( 2. )1,8( 3. )8,1( 4. )0,15(

Pra Fun Math 6 ---------------------------------------------------------------------------------------------------------------------------------------------------------

9. 1|),(

1|),(

17|),(

22

22

22

xyyxB

yxyxA

yxyxS

ASp BSq

p q

1. 423 2. 223 3. 232 4. 332

10. xy 82 62 yx

1. 52 2. 25 3. 5

2 4. 5

2

11. E C 122 yx E C (1, 0) E

1. )2

3,

2

1( 2. )

2

5,

2

1( 3. )

3

2,

3

1( 4. )

3

4,

3

1(

PAT1 .. 52

12. A = {(x, y) | x2 + y2 = 1} B = {(x, y) | x2 + y2 10x 10y + 49 = 0} p A q B p q 1. 25 2. 252 3. 52 4. 525

13. E x2 y2 = 1 E (0, 1) E

1. )2

2,1( 2. )2,1( 3. )

2

1,1( 4. )

2

3,1(

14. a, b c x2 + y2 + ax + by + c = 0 (2, 1) x y + 2 = 0 | a + b + c |

15. (-1, 0) y = x P Q P Q

PAT1 .. 53

16. 404421002125 22 yxyx = 0 )81,3( 1. 0253281045 22 yxyx 2. 01588623 22 yxyx 3. 0191624 22 yxyx 4. 0282827 22 yxyx

Pra Fun Math 7 ---------------------------------------------------------------------------------------------------------------------------------------------------------

17. A(-3, 1) B(1, 5) C(8, 3) D(2, -3) ABCD 1. AB DC 2. AB DC 210

3. A C D 2

29

4. B C D 2

9

18. ABC A(0, 0) B(2, 2) C(x, y) (quadrant) 2 AC BC ABC 4 C 1. x y + 4 = 0 2. 4x + 3y 1 = 0 3. 2x y 3 = 0 4. x + y 5 = 0

PAT1 .. 53

19. 0176490169 22 yxyx

1. 4

25 2. 2

25 3. 4 4. 5

20. ABC CBA 10 A B (-4, 3) (-1, 2) C 1. 0278 yx 2. 0278 yx 3. 0354 yx 4. 0345 yx

PAT1 .. 53

21. . x2 + y2 + 6x 4y = 23 21x + 20y + 168 = 0 . y2 + 16x 6y = 71 (-5, 3) (-1, 3) 1. . . 2. . . 3. . . 4. . .

22. ABCD A(-2, 3) B(2, 8) C(4, 4) D(0, -3) ABCD 1. 16 2. 32 3. 1310 4. 1026

23. A(1, 0) B(b, 0) b > 1 L (-1, 0)

3

4 b

Pra Fun Math 8 ---------------------------------------------------------------------------------------------------------------------------------------------------------

PAT1 .. 54

24. x y + 2 = 0 x2 + y2 + 6x 4y + 4 = 0 A B (a, b) y = 2 A B a + b

1. 4

11 2. 4

9 3. 4

7 4. 4

5

25. . 4x2 25y2 + 24x 100y 164 = 0 4x2 + 252 + 24x + 100y + 36 = 0 . 4x2 + 252 + 24x + 100y + 36 = 0 y2 + 4y 4x + 12 = 0 1. . . 2. . . 3. . . 4. . .

26. a > tan 60o A(a, 3) , B(7, 8) C(-4, 9) A L A B k ky = x2 + 2k L

PAT1 .. 54

27. P x2 + y2 + 2x 4y 15 = 0 A(1, 3) P 3y 4x = 15 1. 3 2. 3.2 3. 3.4 4. 3.5

28. (-3, -2) 5x2 4y2 16y + 4 = 0 1. 4y + 15 = 0 2. 4y + 9 = 0 3. 4x + 9 = 0 4. 4x + 15 = 0

29. M(a, b) xy = 6 x y 1 = 0 M 6x 8y + 13 = 0

PAT1 .. 55

30. x y 12 10 1. 5x2 + 9y2 = 405 2. 9x2 + 5y2 = 81 3. 5x2 + 9y2 = 225 4. 9x2 + 5y2 = 20

Pra Fun Math 9 ---------------------------------------------------------------------------------------------------------------------------------------------------------

31. F x2 + y2 6x + 4y + 4 = 0 V y A B AB F VAB 1. 9 2. 12 3. 18 4. 36

PAT1 .. 55

32. 2522 yx 07622 yyx 032 x 1. 084 22 xyx 2. 020244 22 yyx 3. 0764 22 yyx 4. 048324 22 xyx

33. ),( khC 04 yx )2,5( A )5,2(B ABC

PAT1 .. 56

34. P 04622 xyy P 0623 yx 3,4 1. 05582477 22 yxyx 2. 05582477 22 yxyx 3. 05582477 22 yxyx 4. 05582477 22 yxyx

35. 01996418169 22 yxyx y x (1,0)

1.

8

1,2 2.

2

1,1 3.

2

1,3 4.

4

1,4

36. )0,0( 1F 2F x )1,4(A

)1,4(A 26 L x )0,5.4( )1,4(A d )0,0( L 21

2 AFAFd

PAT1 .. 57

37. L 1b

y

a

x 0, ba 1C 2C

L 1C (0, 0)

2C 1. 03))((4)()( 222222222 baaybxbaabyxba 2. 03)(4))(( 222222 baaybxabyxba 3. 05))((4)()( 222222222 baaybxbaabyxba 4. 05)(4))(( 222222 baaybxabyxba

Pra Fun Math 10 ---------------------------------------------------------------------------------------------------------------------------------------------------------

38. x2 y2 2x = 0 y = 2x 1. 9x2 + 12x + 12y 3 = 0 2. 9x2 + 12x + 12y + 8 = 0 3. 9x2 + 6x 12y 3 = 0 4. 9x2 + 6x + 12y + 5 = 0

39. . P(x, y) P(x, y) (0, -2) P(x, y) (2, -2) 52 P(x, y) { (x, y) | 4x2 + 5y2 8x + 20y 12 = 0 } . (1, 1) y = x2 y = 2x 4 1. . . 2. . . 3. . . 4. . .

PAT1 .. 57

40. F 1364 2 xxy . Y . F . 322,3 . 12 1. 0144362494 22 yxyx 2. 036362494 22 yxyx 3. 0144362449 22 yxxy 4. 036362449 22 yxxy

41. 09222 CyBxAyx (2, 1) 2 1. 0 CBA

2. 5

3

3. 0202422 yxyx 4. (2, 6) 20

42. A 013 yx 0952 yx L m m < 0 (0, 0) k k2 + 2m = 1 A L 1. 052 yx 2. 073 yx 3. 042 yx 4. 053 yx

Pra Fun Math 11 ---------------------------------------------------------------------------------------------------------------------------------------------------------

PAT1 .. 57

43. 0682 22 xxy 2y A B B A 2y P Q Q P P Q A B 1. 042482 22 yxyx 2. 082282 22 yxyx 3. 062442 22 yxyx 4. 062442 22 yxyx

44. C 022 FEyDxyx (quadrant) 1 C y P FEyyDx 2 (-4, -1) 1 . 133222 FED . 0734 yx C 1. . . 2. . . 3. . . 4. . .

45. L1 (-2, -4) X Y A B X Y 3 L2 L1 (0, -13) C L2 CA = CB ABC 1. 8.5 2. 7.5 3. 6.5 4. 5.5

PAT1 .. 58

46. 2 216 9 36 32 124 0y x x y L (0, 0) L

1. 2 5 2. 3 5 3. 4 5 4. 5 5

47. ( , )a b 2 6 0y x (3,1) ( , )a b x 1. 2 2 8 2 16 0x y x y 2. 2 2 8 2 1 0x y x y 3. 2 2 4 2 16 0x y x y 4. 2 2 4 2 1 0x y x y

48. (8, 0) (4, -1) (1, -1) (quardrant) 1 1. 2 8 4 13 0x x y 2. 2 8 4 20 0x x y 3. 2 8 6 12 0x x y 4. 2 8 6 19 0x x y

Pra Fun Math 12 ---------------------------------------------------------------------------------------------------------------------------------------------------------

A NET

A NET 49

1. 9x2 + 4y2 36x 24y + 36 = 0 (1, 3) (5, 0)

1. 5

3 2. 5

4 3. 8

7 4. 13

9

2. H 16x2 9y2 144 = 0 A(6, k) k > 0 H F1 , F2 H AF1F2

1. 2

37 2. 2

45 3. 30 4. 40

A NET 50

3. k, l m kx2 + ly2 72x 24y + m = 0 (4, 3) Y 1. 12 2. 8 3. 54 4. (2, 6)

4. C (x 2)2 = 8y C P Q R 4 PQR 1. 8 2. 9 3. 10 4. 12

5. 16x2 9y2 + 32x + 36y = 164 X x1, x2 x1, x2

A NET 51

6. A B 4x2 y2 24x + 6y + 11 = 0 AB X 1. (x 3)2 = 4(y 2) 2. (x 3)2 = 8(y 1) 3. (x 2)2 = 4(y 2) 4. (x 2)2 = 8(y 1)

7. E X , (-2, 1) , x = 1 y = 3 1F 2F E C

21FF E C P, Q, R S PQRS

1. 5

12 2. 5

24 3. 5

36 4. 5

48

Pra Fun Math 13 ---------------------------------------------------------------------------------------------------------------------------------------------------------

1

49

1. Y 6 0.8 m > 0 2x2 y2 8x + 2y + 5 = 0

2. O R < 10 (-1, 8) X Y A B OAB 1. 10.5 2. 12.5 3. 14.5 4. 16.5

50

3. 9(x 2)2 16(y 1)2 + 144 = 0 (4, 2) 1. 0.2 2. 0.4 3. 0.6 4. 0.8

51

4. 2 2

19 4

x y A(x1, y1) B(x2, y2) x2 > 0

B y = x + 3

1. x2 + (y 2)2 = 2 2. x2 + (y 2)2 = 12

3. (x 3)2 + y2 = 3 4. (x 3)2 + y2 = 18

5. 6 (-6, 0) y2 = -8x

1. 2 2( 2)

19 7

x y 2.

2 2( 2)1

9 10

x y

3. 2 2( 2)

19 55

x y 4.

2 2( 2)1

9 28

x y

6. L1 : 2x + 3y = 12 L2 : 2x + y = 8 (3, 2) cos

1. 165

2. 165

3. 765

4. 765

Pra Fun Math 14 ---------------------------------------------------------------------------------------------------------------------------------------------------------

52

7. L x2 + y2 = 4 (x 5)2 + y2 = 9 30o x = 5 L

1. 1 23 3

y x 2. 1 23 3

y x

3. 3 2 3y x 4. 3 2 3y x

8. ( , 0)c ( ( 1), 0)c c x2 + 12y = 0 1. 5x2 + 9y2 = 45 2. 7x2 + 16y2 = 112 3. 9x2 + 25y2 = 225 4. 13x2 + 36y2 = 468

9. L m 2

2 ( 1)( 2) 14

yx

m

L 1. m = 0.5 2. m = 1.0 3. m = 1.5 4. m = 2.5

53

10. y = 5x2 4x + c X c

1. 45

2. 0 3. 45

4. 25

54

11. P(x, y) x2 + y2 = 1 A(3, 4) P(x, y) 4x 3y + 1 = 0

12. 1F

2F 9x2 16y2 18x + 32y 151 = 0 C

1 2F F

C 1. x2 + y2 + 2x + 2y 23 = 0 2. x2 + y2 2x 2y 23 = 0 3. x2 + y2 + 2x + 2y 14 = 0 4. x2 + y2 2x 2y 14 = 0

55

13.

1. 2 4 24 0x y 2. 2 2

125 16

x y ; 0x

3. 2 2

125 16

x y ; 0x 4. 2 2 2 10 23 0x y x y

Pra Fun Math 15 ---------------------------------------------------------------------------------------------------------------------------------------------------------

56

14. 11 , 03

2 2

3 21( , ) 1

5 20x y x y

10,4

15. a) b) Ax2 + By2 + Cx + Dy + E = 0 A B C D E A B c) x2 + y2 = 9 x2 + y2 3x = 0 Y d) xy x y = 0 13 1 1. a) b) 2. a) c) 3. b) c) 4. c) d)

58

16. x2 + y2 + 2y 6x 15 = 0 Y () (0, -1) 1. 16x2 + 25y2 96x + 50y 231 = 0 2. 16x2 + 25y2 96x + 50y 230 = 0 3. 25x2 + 16y2 150x + 32y 59 = 0 4. 25x2 + 16y2 150x + 32y 60 = 0