11X1 T12 01 locus (2011)

Download 11X1 T12 01 locus (2011)

Post on 28-Jan-2018

684 views

Category:

Education

2 download

TRANSCRIPT

1. Locus 2. LocusLocusThe collection of all points whose location is determined by somestated law. 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 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 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 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 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 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 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 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 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 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 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 14. (ii) A point moves so that it is always 5 units away from the y axis 15. (ii) A point moves so that it is always 5 units away from the y axis y x 16. (ii) A point moves so that it is always 5 units away from the y axis y P x, y x 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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. 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 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 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 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 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 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 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 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 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). 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 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 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 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 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 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 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 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 51. 2y 1 x 3 3 52. 2 y 1 x 3 33y 3 2x 62x 3y 9 0 53. 2 y 1 x 3 33y 3 2x 62x 3y 9 0 OR 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 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 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 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 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