The document defines locus as the collection of all points whose location is determined by some stated law. It then provides examples of finding the locus of points that satisfy specific conditions: (1) always being 4 units from the origin, forming a circle; (2) always being 5 units from the y-axis, forming two lines; (3) always being 3 units from the line y=x+1, forming two parabolas. Finally, it gives an example of a point whose distance from the x-axis is always 5 times its distance from the y-axis.

1. Locus

2. Locus
The collection of all points whose location is determined by some
stated law.
Locus

3. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
Locus

4. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
y
x
Locus

5. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
y
x4
Locus

6. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
y
x4
4
Locus

7. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
y
x4–4
4
Locus

8. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
y
x4–4
4
–4
Locus

9. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
y
x4–4
4
–4
Locus

10. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
y
x4–4
4
–4
Locus

11. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
y
x4–4
4
–4
 yxP ,
Locus

12. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
y
x4–4
4
–4
 yxP ,
    400
22
 yx
Locus

13. Locus
The collection of all points whose location is determined by some
stated law.
e.g. (i) Find the locus of the point which is always 4 units from the
origin
y
x4–4
4
–4
 yxP ,
    400
22
 yx
1622
 yx
Locus

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
x
 yxP ,

17. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y

18. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   

19. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 

20. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  

21. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(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 axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x

23. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x
1y x 
1
–1

24. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x
1y x 
1
–1
 yxP ,

25. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x
1y x 
1
–1
 yxP ,

26. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x
1y x 
1
–1
 yxP ,
 
22
1
3
1 1
x y 

 

27. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x
1y x 
1
–1
 yxP ,
 
22
1
3
1 1
x y 

 
1 3 2x y  

28. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x
1y x 
1
–1
 yxP ,
 
22
1
3
1 1
x y 

 
1 3 2x y  
1 3 2x y  

29. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x
1y x 
1
–1
 yxP ,
 
22
1
3
1 1
x y 

 
1 3 2x y  
1 3 2x y    1 3 2or x y   

30. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x
1y x 
1
–1
 yxP ,
 
22
1
3
1 1
x y 

 
1 3 2x y  
1 3 2x y    1 3 2or x y   
1 3 2 0x y   

31. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x
1y x 
1
–1
 yxP ,
 
22
1
3
1 1
x y 

 
1 3 2x y  
1 3 2x y    1 3 2or x y   
1 3 2 0x y    1 3 2x y   

32. (ii) A point moves so that it is always 5 units away from the y axis
y
x
 yxP ,5 0, y
   
2 2
0 5x y y   
2
25x 
5x  
(iii) A point moves so that it is always 3 units away from the line y = x + 1
y
x
1y x 
1
–1
 yxP ,
 
22
1
3
1 1
x y 

 
1 3 2x y  
1 3 2x y    1 3 2or x y   
1 3 2 0x y    1 3 2x y   
1 3 2 0x y   

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.
y
x
 yxP ,

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.
y
x
 yxP ,
 ,0x

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.
y
x
 yxP , 0, y
 ,0x

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.
y
x
 yxP ,d 0, y
5d
 ,0x

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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
5d
 ,0x

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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5d
 ,0x

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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5y x 
5d
 ,0x

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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5y x 
(v) A point moves so that its distance from (1,2) is the same as its
distance from (5,–4).
5d
 ,0x

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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5y x 
(v) A point moves so that its distance from (1,2) is the same as its
distance from (5,–4).
y
x
5d
 ,0x

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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5y x 
(v) A point moves so that its distance from (1,2) is the same as its
distance from (5,–4).
y
x
5d
 ,0x
 1,2
 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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5y x 
(v) A point moves so that its distance from (1,2) is the same as its
distance from (5,–4).
y
x yxP ,
5d
 ,0x
 1,2
 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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5y x 
(v) A point moves so that its distance from (1,2) is the same as its
distance from (5,–4).
y
x yxP ,
5d
 ,0x
 1,2
 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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5y x 
(v) A point moves so that its distance from (1,2) is the same as its
distance from (5,–4).
y
x yxP ,
5d
 ,0x
 1,2
 5, 4
Perpendicular bisector of (1,2) and (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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5y x 
(v) A point moves so that its distance from (1,2) is the same as its
distance from (5,–4).
y
x yxP ,
5d
 ,0x
 1,2
 5, 4
Perpendicular bisector of (1,2) and (5,–4)
4 2
5 1
6
4
3
2
ABm
 







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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5y x 
(v) A point moves so that its distance from (1,2) is the same as its
distance from (5,–4).
y
x yxP ,
5d
 ,0x
 1,2
 5, 4
Perpendicular bisector of (1,2) and (5,–4)
4 2
5 1
6
4
3
2
ABm
 






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.
y
x
 yxP ,d 0, y
       
2 2 2 2
0 5 0x x y x y y      
2 2
25y x
5y x 
(v) A point moves so that its distance from (1,2) is the same as its
distance from (5,–4).
y
x yxP ,
5d
 ,0x
 1,2
 5, 4
Perpendicular bisector of (1,2) and (5,–4)
4 2
5 1
6
4
3
2
ABm
 






 
1 5 4 2
,
2 2
3, 1
ABM
   
  
 
 
2
required slope
3
 

51.  
2
1 3
3
y x  

52.  
2
1 3
3
y x  
3 3 2 6
2 3 9 0
y x
x y
  
  

53. OR
 
2
1 3
3
y x  
3 3 2 6
2 3 9 0
y x
x y
  
  

54.        
2 2 2 2
1 2 5 4x y x y      
OR
 
2
1 3
3
y x  
3 3 2 6
2 3 9 0
y x
x y
  
  

55.        
2 2 2 2
1 2 5 4x y x y      
2 2 2 2
2 1 4 4 10 25 8 16x x y y x x y y          
OR
 
2
1 3
3
y x  
3 3 2 6
2 3 9 0
y x
x y
  
  

56.        
2 2 2 2
1 2 5 4x y x y      
2 2 2 2
2 1 4 4 10 25 8 16x x y y x x y y          
8 12 36 0x y  
OR
 
2
1 3
3
y x  
3 3 2 6
2 3 9 0
y x
x y
  
  

57.        
2 2 2 2
1 2 5 4x y x y      
2 2 2 2
2 1 4 4 10 25 8 16x x y y x x y y          
8 12 36 0x y  
2 3 9 0x y  
OR
 
2
1 3
3
y x  
3 3 2 6
2 3 9 0
y x
x y
  
  

58.        
2 2 2 2
1 2 5 4x y x y      
2 2 2 2
2 1 4 4 10 25 8 16x x y y x x y y          
8 12 36 0x y  
2 3 9 0x y  
OR
 
2
1 3
3
y x  
3 3 2 6
2 3 9 0
y x
x y
  
  
Exercise 9A; 1aceg, 3a, 4, 6, 8, 10, 11, 13, 14