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 |