11X1 T11 02 parabola as a locus (2011)

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<ul><li> 1. The Parabola As a Locus yx</li></ul><p> 2. The Parabola As a Locus yA point moves so that its distancefrom a fixed point (focus) isequal to its distance from a fixedline (directrix)x 3. The Parabola As a Locus yA point moves so that its distancefrom a fixed point (focus) isequal to its distance from a fixed S 0, a line (directrix)x 4. The Parabola As a Locus yA point moves so that its distancefrom a fixed point (focus) isequal to its distance from a fixed S 0, a line (directrix)xy a 5. The Parabola As a Locus yA point moves so that its distancefrom a fixed point (focus) isequal to its distance from a fixed S 0, a line (directrix)xy a 6. The Parabola As a Locus y A point moves so that its distance from a fixed point (focus) is equal to its distance from a fixed S 0, a P x, y line (directrix) xy a 7. The Parabola As a Locus y A point moves so that its distance from a fixed point (focus) is equal to its distance from a fixed S 0, a P x, y line (directrix) xy aM ( x, a) 8. The Parabola As a Locus y A point moves so that its distance from a fixed point (focus) is equal to its distance from a fixed S 0, a P x, y line (directrix) xy aM ( x, a) d PS d PM 9. The Parabola As a Locus y A point moves so that its distance from a fixed point (focus) is equal to its distance from a fixed S 0, a P x, y line (directrix) xy aM ( x, a)d PS d PM x 0 y a x x y a 2 2 22 10. The Parabola As a Locus y A point moves so that its distance from a fixed point (focus) is equal to its distance from a fixed S 0, a P x, y line (directrix) xy aM ( x, a)d PS d PM x 0 y a x x y a 2 2 22 x2 y a y a 2 2 11. The Parabola As a Locus y A point moves so that its distance from a fixed point (focus) is equal to its distance from a fixed S 0, a P x, y line (directrix) xy aM ( x, a)d PS d PM x 0 y a x x y a 2 2 22 x2 y a y a 2 2 x 2 y 2 2ay a 2 y 2 2ay a 2 12. The Parabola As a Locus y A point moves so that its distance from a fixed point (focus) is equal to its distance from a fixed S 0, a P x, y line (directrix) xy aM ( x, a)d PS d PM x 0 y a x x y a 2 2 22 x2 y a y a 2 2 x 2 y 2 2ay a 2 y 2 2ay a 2 x 2 4ay 13. x 2 4ay 14. x 2 4ayvertex: 0,0 15. x 2 4ayvertex: 0,0 focus: 0, a 16. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a 17. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a units 18. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 y 19. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 y 4a 32 20. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 y 4a 32 a 8 21. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 y 4a 32 a 8focal length = 8 units 22. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 y 4a 32 a 8focal length = 8 units 23. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 y 4a 32 a 8(0,0)focal length = 8 units 24. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 y 4a 32 8 a 8(0,0)focal length = 8 units 25. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 32 8 a 8(0,0)focal length = 8 units 26. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 32 8 a 8(0,0) 8focal length = 8 units 27. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 32 8 a 8directrix is y 8 (0,0) 8focal length = 8 units 28. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 32 8 a 8directrix is y 8 (0,0) 8focal length = 8 units b) y 4 x 2 29. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 32 8 a 8directrix is y 8 (0,0) 8focal length = 8 units1 b) y 4 x 2 x 2 y4 30. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 32 8 a 8directrix is y 8 (0,0) 8focal length = 8 units1 b) y 4 x 2 x 2 y1 4 4a 4 31. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 32 8 a 8directrix is y 8 (0,0) 8focal length = 8 units1 b) y 4 x 2 x 2 y1 4 4a 41a 16 32. x 2 4ay vertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 328 a 8directrix is y 8(0,0) 8focal length = 8 units1 b) y 4 x 2 x 2 y1 4 4a 41afocal length =1 unit 1616 33. x 2 4ay vertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 328 a 8directrix is y 8(0,0) 8focal length = 8 units1 b) y 4 x 2 x 2 y1 4 4a 41afocal length =1 unit 1616 34. x 2 4ay vertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 328 a 8directrix is y 8(0,0) 8focal length = 8 units1 b) y 4 x 2 x 2 y1 4 4a 41 (0,0)afocal length =1 unit 1616 35. x 2 4ay vertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 yfocus is (0,8) 4a 328 a 8directrix is y 8(0,0) 8focal length = 8 units1 b) y 4 x 2 x 2 y1 4 4a 14 161 (0,0)afocal length =1 unit 1616 36. x 2 4ay vertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 y focus is (0,8) 4a 328 a 8directrix is y 8(0,0) 8focal length = 8 units 11focus is 0, b) y 4 x x y22 16 1 4 4a 14 161 (0,0)afocal length =1 unit 1616 37. x 2 4ay vertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 y focus is (0,8) 4a 328 a 8directrix is y 8(0,0) 8focal length = 8 units 11focus is 0, b) y 4 x x y22 16 1 4 4a 14 161 (0,0)a 11 16 16 focal length = unit 16 38. x 2 4ay vertex: 0,0 focus: 0, a directrix: y a focal length: a unitse.g. (i) Find the focus, focal length and directrix;a) x 2 32 y focus is (0,8) 4a 328 a 8directrix is y 8(0,0) 8focal length = 8 units 11focus is 0, b) y 4 x x y22 16 1 4 4a 14 directrix is y 1116 16a1 (0,0)116 16 focal length = unit 16 39. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 40. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 a 2 41. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 a 2 x 2 4 2 y 42. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 a 2 x 2 4 2 yx 2 8 y 43. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3 a 2x 2 4 2 y x 2 8 y 44. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3 a 2x 2 4 2 y a3 x 2 8 y 45. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3 a 2x 2 4 2 y a3y 2 4 3 x x 2 8 y 46. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3 a 2x 2 4 2 y a3y 2 4 3 x x 2 8 y y 2 12 x 47. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3 a 2x 2 4 2 y a3y 2 4 3 x x 2 8 y y 2 12 xVertex NOT at the origin 48. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3 a 2x 2 4 2 ya3 y 2 4 3 x x 2 8 yy 2 12 xVertex NOT at the origin x p 4a y q 2 49. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3 a 2x 2 4 2 ya3 y 2 4 3 x x 2 8 yy 2 12 xVertex NOT at the origin x p 4a y q 2vertex: p, q 50. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3 a 2x 2 4 2 ya3 y 2 4 3 x x 2 8 yy 2 12 xVertex NOT at the origin x p 4a y q 2vertex: p, q focus: p, q a 51. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3 a 2x 2 4 2 ya3 y 2 4 3 x x 2 8 yy 2 12 xVertex NOT at the origin x p 4a y q 2vertex: p, q focus: p, q a directrix: y q a 52. (ii) Find the equation of the parabola with;a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3 a 2x 2 4 2 ya3 y 2 4 3 x x 2 8 yy 2 12 xVertex NOT at the origin x p 4a y q 2vertex: p, q focus: p, q a directrix: y q afocal length: a units 53. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units 54. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 55. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 2 x 3 8 y 1 2x2 6 x 9 8 y 8 56. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 2 x 3 8 y 1 2x2 6 x 9 8 y 8 8 y x 2 6 x 17 y x 6 x 17 1 28 57. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 x 3 4 2 y 1 22 x 3 8 y 1 2x2 6 x 9 8 y 8 8 y x 2 6 x 17 y x 6 x 17 1 28 58. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 x 3 4 2 y 1 2 2 x 3 8 y 1 x 3 8 y 1 2 2x2 6 x 9 8 y 8x 2 6 x 9 8 y 8 8 y x 2 6 x 17 y x 6 x 17 1 28 59. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 x 3 4 2 y 1 2 2 x 3 8 y 1 x 3 8 y 1 2 2x2 6 x 9 8 y 8x 2 6 x 9 8 y 8 8 y x 2 6 x 17 8 y x2 6x 1 y x 6 x 17 y x 6 x 11 2 1 28 8 60. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 x 3 4 2 y 1 2 2 x 3 8 y 1 x 3 8 y 1 2 2x2 6 x 9 8 y 8x 2 6 x 9 8 y 8 8 y x 2 6 x 17 8 y x2 6x 1 y x 6 x 17 y x 6 x 11 2 1 28 8 y 1 4 2 x 32 61. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 x 3 4 2 y 1 2 2 x 3 8 y 1 x 3 8 y 1 2 2x2 6 x 9 8 y 8x 2 6 x 9 8 y 8 8 y x 2 6 x 17 8 y x2 6x 1 y x 6 x 17 y x 6 x 11 2 1 28 8 y 1 4 2 x 32 y 1 8 x 3 2y 2 2 y 1 8 x 24 62. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 x 3 4 2 y 1 2 2 x 3 8 y 1 x 3 8 y 1 2 2x2 6 x 9 8 y 8x 2 6 x 9 8 y 8 8 y x 2 6 x 17 8 y x2 6x 1 y x 6 x 17 y x 6 x 11 2 1 28 8 y 1 4 2 x 32 y 1 8 x 3 2y 2 2 y 1 8 x 248 x y 2 2 y 25x y 2 y 25 1 2 8 63. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 x 3 4 2 y 1 2 2 x 3 8 y 1 x 3 8 y 1 2 2x2 6 x 9 8 y 8x 2 6 x 9 8 y 8 8 y x 2 6 x 17 8 y x2 6x 1 y x 6 x 17 y x 6 x 11 2 1 28 8 y 1 4 2 x 3 y 1 4 2 x 322 y 1 8 x 3 2y 2 2 y 1 8 x 248 x y 2 2 y 25x y 2 y 25 1 2 8 64. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 x 3 4 2 y 1 2 2 x 3 8 y 1 x 3 8 y 1 2 2x2 6 x 9 8 y 8x 2 6 x 9 8 y 8 8 y x 2 6 x 17 8 y x2 6x 1 y x 6 x 17 y x 6 x 11 21 288 y 1 4 2 x 3 y 1 4 2 x 322 y 1 8 x 3 y 1 8 x 3 2 2y 2 2 y 1 8 x 24 y 2 2 y 1 8 x 248 x y 2 2 y 25x y 2 y 25 1 2 8 65. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 x 3 4 2 y 1 2 2 x 3 8 y 1 x 3 8 y 1 2 2x2 6 x 9 8 y 8x 2 6 x 9 8 y 8 8 y x 2 6 x 17 8 y x2 6x 1 y x 6 x 17 y x 6 x 11 21 288 y 1 4 2 x 3 y 1 4 2 x 322 y 1 8 x 3 y 1 8 x 3 2 2y 2 2 y 1 8 x 24 y 2 2 y 1 8 x 248 x y 2 2 y 25 8 x y 2 2 y 23x y 2 y 25 x y 2 y 23 1 21 2 88 66. (ii) focus (2,8) and directrix y = 10 67. (ii) focus (2,8) and directrix y = 10 68. (ii) focus (2,8) and directrix y = 10a y 10 69. (ii) focus (2,8) and directrix y = 10ay 10a 2,8 70. (ii) focus (2,8) and directrix y = 10ay 10a 2,82a 2 a 1 71. (ii) focus (2,8) and directrix y = 10ay 10a 2,82a 2 a 1 vertex is (2,9) 72. (ii) focus (2,8) and directrix y = 10ay 10a 2,82a 2 a 1 vertex is (2,9) x 2 4 1 y 9 2 73. (ii) focus (2,8) and directrix y = 10ay 10a 2,82a 2 a 1 vertex is (2,9) x 2 4 1 y 9 2 x 2 4 y 9 2 74. (ii) focus (2,8) and directrix y = 10ay 10a 2,82a 2 a 1 vertex is (2,9) x 2 4 1 y 9 2 x 2 4 y 9 2x 2 4 x 16 4 y 36 75. (ii) focus (2,8) and directrix y = 10ay 10a 2,82a 2 a 1 vertex is (2,9) x 2 4 1 y 9 2 x 2 4 y 9 2x 2 4 x 16 4 y 36 4 y x 2 4 x 20 y x 4 x 20 1 2 4 76. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 77. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 3 78. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 3 12 y 3 x 2 6 x 79. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 3 12 y 3 x 2 6 x 12 y 3 9 x 3 2 80. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 3 12 y 3 x 2 6 x 12 y 3 9 x 3 212 y 12 x 3 2 81. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 3 12 y 3 x 2 6 x 12 y 3 9 x 3212 y 12 x 32 12 y 1 x 32 82. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 3 12 y 3 x 2 6 x 12 y 3 9 x 3 2 12 y 12 x 3 212 y 1 x 3 24a 83. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 3 12 y 3 x 2 6 x 12 y 3 9 x 3212 y 12 x 32 12 y...</p>