11X1 T12 01 locus (2011)

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<ol><li> 1. Locus </li><li> 2. LocusLocusThe collection of all points whose location is determined by somestated law. </li><li> 3. Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the origin </li><li> 4. Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the originyx </li><li> 5. Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the originy 4x </li><li> 6. Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the originy4 4x </li><li> 7. Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the originy44 4x </li><li> 8. Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the originy44 4x 4 </li><li> 9. Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the originy44 4x 4 </li><li> 10. Locus LocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the originy44 4x 4 </li><li> 11. LocusLocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the originy P x, y 444 x 4 </li><li> 12. LocusLocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the originy P x, y 4 x 02 y 02 444 x 4 </li><li> 13. LocusLocusThe collection of all points whose location is determined by somestated law.e.g. (i) Find the locus of the point which is always 4 units from the originy P x, y 4 x 02 y 02 444 x x 2 y 2 16 4 </li><li> 14. (ii) A point moves so that it is always 5 units away from the y axis </li><li> 15. (ii) A point moves so that it is always 5 units away from the y axis y x </li><li> 16. (ii) A point moves so that it is always 5 units away from the y axis y P x, y x </li><li> 17. (ii) A point moves so that it is always 5 units away from the y axis y 0, y 5 P x, y x </li><li> 18. (ii) A point moves so that it is always 5 units away from the y axis y 0, y 5 P x, y x 0 y y 52 2 x </li><li> 19. (ii) A point moves so that it is always 5 units away from the y axis y 0, y 5 P x, y x 0 y y 52 2 x x 2 25 </li><li> 20. (ii) A point moves so that it is always 5 units away from the y axis y 0, y 5 P x, y x 0 y y 52 2 x x 2 25 x 5 </li><li> 21. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2 xx 2 25 x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1 </li><li> 22. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2 xx 2 25 x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1y x </li><li> 23. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2 xx 2 25 x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1 yy x 1 11 x </li><li> 24. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2x x 2 25 x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1y y x 1 P x, y 1 1 x </li><li> 25. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2x x 2 25 x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1y y x 1 P x, y 1 1 x </li><li> 26. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2xx 2 25x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1y y x 1 x y 1 P x, y 3 12 121 1 x </li><li> 27. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2xx 2 25x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1y y x 1 x y 1 P x, y 3 12 121 x y 1 3 2 1 x </li><li> 28. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2xx 2 25x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1y y x 1 x y 1 P x, y 3 12 121x y 1 3 2 1 x x y 1 3 2 </li><li> 29. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2xx 2 25x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1y y x 1 x y 1 P x, y 3 12 121x y 1 3 2 1 x x y 1 3 2or x y 1 3 2 </li><li> 30. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2xx 2 25x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1y y x 1 x y 1 P x, y 3 12 121x y 1 3 2 1 x x y 1 3 2or x y 1 3 2x y 1 3 2 0 </li><li> 31. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2xx 2 25x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1y y x 1 x y 1 P x, y 3 12 121x y 1 3 2 1 x x y 1 3 2or x y 1 3 2x y 1 3 2 0 x y 1 3 2 </li><li> 32. (ii) A point moves so that it is always 5 units away from the y axisy 0, y 5 P x, y x 0 y y 5 2 2xx 2 25x 5(iii) A point moves so that it is always 3 units away from the line y = x + 1y y x 1 x y 1 P x, y 3 12 121x y 1 3 2 1 x x y 1 3 2or x y 1 3 2x y 1 3 2 0 x y 1 3 2x y 1 3 2 0 </li><li> 33. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis. </li><li> 34. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.y x </li><li> 35. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y x </li><li> 36. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y x,0 x </li><li> 37. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y 0, y x,0 x </li><li> 38. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y 5d x,0 x </li><li> 39. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2222 5d x,0 x </li><li> 40. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x </li><li> 41. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x y 5 x </li><li> 42. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x y 5 x(v) A point moves so that its distance from (1,2) is the same as itsdistance from (5,4). </li><li> 43. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x y 5 x(v) A point moves so that its distance from (1,2) is the same as itsdistance from (5,4).y x </li><li> 44. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x y 5 x(v) A point moves so that its distance from (1,2) is the same as itsdistance from (5,4).y 1, 2 x 5, 4 </li><li> 45. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x y 5 x(v) A point moves so that its distance from (1,2) is the same as itsdistance from (5,4).y1, 2 P x, y x 5, 4 </li><li> 46. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x y 5 x(v) A point moves so that its distance from (1,2) is the same as itsdistance from (5,4).y1, 2 P x, y x 5, 4 </li><li> 47. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x y 5 x(v) A point moves so that its distance from (1,2) is the same as itsdistance from (5,4).y Perpendicular bisector of (1,2) and (5,4)1, 2 P x, y x 5, 4 </li><li> 48. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x y 5 x(v) A point moves so that its distance from (1,2) is the same as itsdistance from (5,4). yPerpendicular bisector of (1,2) and (5,4)4 2 1, 2 mAB 5 1P x, y 6 x4 5, 4 32 </li><li> 49. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x y 5 x(v) A point moves so that its distance from (1,2) is the same as itsdistance from (5,4). yPerpendicular bisector of (1,2) and (5,4) 4 2 1, 2 mAB 5 1P x, y 6 x 4 5, 4 3 2 2 required slope 3 </li><li> 50. (iv) A point moves so that its distance from the x axis is always 5 times as great as its distance from the y axis.P x, y y d 0, y x x y 0 5 x 0 y y 2 2 22 5d y 2 25 x 2 x,0 x y 5 x(v) A point moves so that its distance from (1,2) is the same as itsdistance from (5,4). yPerpendicular bisector of (1,2) and (5,4) 4 2 1, 2 mAB 1 5 4 2 M AB 5 1 , 2 2 P x, y 6 x 3, 1 4 5, 4 3 2 2 required slope 3 </li><li> 51. 2y 1 x 3 3 </li><li> 52. 2 y 1 x 3 33y 3 2x 62x 3y 9 0 </li><li> 53. 2 y 1 x 3 33y 3 2x 62x 3y 9 0 OR </li><li> 54. 2 y 1 x 3 33y 3 2x 62x 3y 9 0 OR x 1 y 2 x 5 y 4 22 2 2 </li><li> 55. 2 y 1 x 3 33y 3 2x 62x 3y 9 0 OR x 1 y 2 x 5 y 4 2 222x 2 2 x 1 y 2 4 y 4 x 2 10 x 25 y 2 8 y 16 </li><li> 56. 2 y 1 x 3 33y 3 2x 62x 3y 9 0 OR x 1 y 2 x 5 y 4 2 222x 2 2 x 1 y 2 4 y 4 x 2 10 x 25 y 2 8 y 168 x 12 y 36 0 </li><li> 57. 2 y 1 x 3 33y 3 2x 62x 3y 9 0OR x 1 y 2 x 5 y 4 222 2x 2 2 x 1 y 2 4 y 4 x 2 10 x 25 y 2 8 y 168 x 12 y 36 02x 3 y 9 0 </li><li> 58. 2 y 1 x 3 33y 3 2x 62x 3y 9 0OR x 1 y 2 x 5 y 4 222 2x 2 2 x 1 y 2 4 y 4 x 2 10 x 25 y 2 8 y 168 x 12 y 36 02x 3 y 9 0 Exercise 9A; 1aceg, 3a, 4, 6, 8, 10, 11, 13, 14</li></ol>