11X1 T12 02 parabola as a locus

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<ul><li> 1. The Parabola As a Locusy x </li></ul><p> 2. The Parabola As a LocusyA point moves so that its distance from a fixed point (focus) is equal to its distance from a fixed line (directrix)x 3. The Parabola As a LocusyA point moves so that its distance from a fixed point (focus) is equal to its distance from a fixedS 0, a line (directrix)x 4. The Parabola As a LocusyA point moves so that its distance from a fixed point (focus) is equal to its distance from a fixedS 0, a line (directrix)xy a 5. The Parabola As a LocusyA point moves so that its distance from a fixed point (focus) is equal to its distance from a fixedS 0, a line (directrix)xy a 6. The Parabola As a Locusy A point moves so that its distancefrom a fixed point (focus) isequal to its distance from a fixedS 0, a P x, y line (directrix) xy a 7. The Parabola As a LocusyA point moves so that its distance from a fixed point (focus) is equal to its distance from a fixedS 0, a P x, y line (directrix)xy aM ( x, a ) 8. The Parabola As a LocusyA point moves so that its distance from a fixed point (focus) is equal to its distance from a fixedS 0, a P x, y line (directrix)xy aM ( x, a ) d PS d PM 9. The Parabola As a LocusyA point moves so that its distance from a fixed point (focus) is equal to its distance from a fixedS 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 LocusyA point moves so that its distance from a fixed point (focus) is equal to its distance from a fixedS 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 LocusyA point moves so that its distance from a fixed point (focus) is equal to its distance from a fixedS 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 2x 2 y 2 2ay a 2 y 2 2ay a 2 12. The Parabola As a LocusyA point moves so that its distance from a fixed point (focus) is equal to its distance from a fixedS 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 2x 2 y 2 2ay a 2 y 2 2ay a 2x 2 4ay 13. x 2 4ay 14. x 2 4ay vertex: 0,0 15. x 2 4ay vertex: 0,0 focus: 0, a 16. x 2 4ay vertex: 0,0 focus: 0, a directrix: y a 17. x 2 4ayvertex: 0,0 focus: 0, a directrix: y a focal length: a units 18. x 2 4ayvertex: 0,0 focus: 0, a directrix: y afocal 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 afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 y4a 32 20. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 y4a 32a 8 21. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 y4a 32a 8 focal length = 8 units 22. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 y4a 32a 8 focal length = 8 units 23. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 y4a 32a 8(0,0) focal length = 8 units 24. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 y4a 328a 8(0,0) focal length = 8 units 25. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 328a 8(0,0) focal length = 8 units 26. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 328a 8(0,0) 8 focal length = 8 units 27. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 328a 8directrix is y 8 (0,0) 8 focal length = 8 units 28. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 328a 8directrix is y 8 (0,0) 8 focal length = 8 unitsb) y 4 x 2 29. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 328a 8directrix is y 8 (0,0) 8 focal length = 8 units 1b) y 4 x 2 x 2 y 4 30. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 328a 8directrix is y 8 (0,0) 8 focal length = 8 units 1b) y 4 x 2 x 2 y 1 44a 4 31. x 2 4ay vertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 328a 8directrix is y 8 (0,0) 8 focal length = 8 units 1b) y 4 x 2 x 2 y 1 44a 4 1 a16 32. x 2 4ayvertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 32 8a 8directrix is y 8(0,0) 8 focal length = 8 units 1b) y 4 x 2 x 2 y 1 44a 4 1 afocal length = 1unit1616 33. x 2 4ayvertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 32 8a 8directrix is y 8(0,0) 8 focal length = 8 units 1b) y 4 x 2 x 2 y 1 44a 4 1 afocal length = 1unit1616 34. x 2 4ayvertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 32 8a 8directrix is y 8(0,0) 8 focal length = 8 units 1b) y 4 x 2 x 2 y 1 44a 4 1 (0,0) afocal length = 1unit1616 35. x 2 4ayvertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 yfocus is (0,8)4a 32 8a 8directrix is y 8(0,0) 8 focal length = 8 units 1b) y 4 x 2 x 2 y 1 44a 1 4 16 1 (0,0) afocal length = 1unit1616 36. x 2 4ayvertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 y focus is (0,8)4a 32 8a 8directrix is y 8(0,0) 8 focal length = 8 units 0, 1 focus is b) y 4 x x y21 16 2 1 44a 1 4 16 1 (0,0) afocal length = 1unit1616 37. x 2 4ayvertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 y focus is (0,8)4a 32 8a 8directrix is y 8(0,0) 8 focal length = 8 units 0, 1 focus is b) y 4 x x y21 16 2 1 44a 1 4 16 1 (0,0) a1 1 1616 focal length = unit16 38. x 2 4ayvertex: 0,0 focus: 0, a directrix: y afocal length: a unitse.g. (i) Find the focus, focal length and directrix; a) x 2 32 y focus is (0,8)4a 32 8a 8directrix is y 8(0,0) 8 focal length = 8 units 0, 1 focus is b) y 4 x x y21 16 2 1 44a 1 4 directrix is y 1116 16a1 (0,0)1 1616 focal length = unit16 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 2a 2 41. (ii) Find the equation of the parabola with; a) focus 0, 2 , directrix y 2a 2 x 2 4 2 y 42. (ii) Find the equation of the parabola with; a) focus 0, 2 , directrix y 2a 2 x 2 4 2 y x 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 3a 2x 2 4 2 yx 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 3a 2x 2 4 2 y a3x 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 3a 2x 2 4 2 y a3y 2 4 3 xx 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 3a 2x 2 4 2 y a3y 2 4 3 xx 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 3a 2x 2 4 2 y a3y 2 4 3 xx 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 3a 2x 2 4 2 ya3 y 2 4 3 xx 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 3a 2x 2 4 2 ya3 y 2 4 3 xx 2 8 yy 2 12 xVertex NOT at the origin x p 4a y q 2 vertex: p, q 50. (ii) Find the equation of the parabola with; a) focus 0, 2 , directrix y 2 b) focus 3,0 , directrix x 3a 2x 2 4 2 ya3 y 2 4 3 xx 2 8 yy 2 12 xVertex NOT at the origin x p 4a y q 2 vertex: 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 3a 2x 2 4 2 ya3 y 2 4 3 xx 2 8 yy 2 12 xVertex NOT at the origin x p 4a y q 2 vertex: 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 3a 2x 2 4 2 ya3 y 2 4 3 xx 2 8 yy 2 12 xVertex NOT at the origin x p 4a y q 2 vertex: p, q focus: p, q a directrix: y q a focal length: a units 53. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units 54. e.g. (i) Find the equation of the parabola with vertex 3,1 andfocal length 2 units x 3 4 2 y 1 2 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 2 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 6x 9 8 y 8 57. 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 6x 9 8 y 8 8 y x 2 6 x 17y x 6 x 17 1 2 8 58. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 12 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 59. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 12 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 60. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 12 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 a y 10 61. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 12 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 ay 10 a 2,8 62. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 12 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 ay 10 a 2,8 2a 2 63. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 12 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 ay 10 a 2,8 2a 2 a 1 64. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 12 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 ay 10 a 2,8 2a 2 a 1 vertex is (2,9) 65. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 1 2 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 x 2 4 1 y 9 2 a y 10 a 2,82a 2a 1 vertex is (2,9) 66. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 1 2 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 x 2 4 1 y 9 2 a y 10 x 2 4 y 9 2 a 2,82a 2a 1 vertex is (2,9) 67. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 12 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 x 2 4 1 y 9 2 ay 10 x 2 4 y 9 2a 2,8x 2 4 x 16 4 y 362a 2a 1 vertex is (2,9) 68. e.g. (i) Find the equation of the parabola with vertex 3,1 and focal length 2 units x 3 4 2 y 12 x 3 8 y 12 x2 6x 9 8 y 88 y x 2 6 x 17 y x 6 x 17 1 28 (ii) focus (2,8) and directrix y = 10 x 2 4 1 y 9 2 ay 10 x 2 4 y 9 2a 2,8x 2 4 x 16 4 y 36 4 y x 2 4 x 20 2a 2 y x 4 x 20 1 2a 1 vertex is (2,9)4 69. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 70. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 3 71. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 312 y 3 x 2 6 x 72. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 312 y 3 x 2 6 x12 y 3 9 x 32 73. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 312 y 3 x 2 6 x12 y 3 9 x 32 12 y 12 x 32 74. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 312 y 3 x 2 6 x12 y 3 9 x 3 2 12 y 12 x 3 212 y 1 x 3 2 75. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 312 y 3 x 2 6 x12 y 3 9 x 3212 y 12 x 32 12 y 1 x 32 4a 76. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 312 y 3 x 2 6 x12 y 3 9 x 3 2 12 y 12 x 3 212 y 1 x 3 2 4a 12 77. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 312 y 3 x 2 6 x12 y 3 9 x 3 2 12 y 12 x 3 212 y 1 x 3 2 4a 12a3 78. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 312 y 3 x 2 6 x12 y 3 9 x 3 2 12 y 12 x 3 212 y 1 x 3 2 4a 12a3 focal length = 3 units 79. (iii) Find the vertex, focus, focal length, directrix of 12 y x 2 6 x 3 12 y x 2 6 x 312 y 3 x 2 6 x12 y 3 9 x 3 2 12 y 12 x 3 212 y 1 x 3 2 4a 12a3 vertex: (3, focal length = 3 units 80. (iii) Find the ver...</p>