Locus
Locus
The collection of all points whose location is determined by some
stated law.
Locus
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
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
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 4
Locus
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 4
4
Locus
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 4 –4
4
Locus
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 4 –4
4
–4
Locus
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 4 –4
4
–4
Locus
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 4 –4
4
–4
Locus
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 4 –4
4
–4
yxP ,
Locus
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 4 –4
4
–4
yxP ,
40022 yx
Locus
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 4 –4
4
–4
yxP ,
40022 yx
1622 yx
Locus
(ii) A point moves so that it is always 5 units away from the y axis
(ii) A point moves so that it is always 5 units away from the y axis
y
x
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 5x y y
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 5x y y
2 25x
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 5x y y
2 25x
5x
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 5x y y
2 25x
5x
(iii) A point moves so that it is always 3 units away from the line y = x + 1
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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 ,
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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 ,
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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
13
1 1
x y
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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
13
1 1
x y
1 3 2x y
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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
13
1 1
x y
1 3 2x y
1 3 2x y
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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
13
1 1
x y
1 3 2x y
1 3 2x y 1 3 2or x y
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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
13
1 1
x y
1 3 2x y
1 3 2x y 1 3 2or x y
1 3 2 0x y
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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
13
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
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
2 20 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
13
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
(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.
(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
(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 ,
(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
(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
(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
(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 20 5 0x x y x y y
5d
,0x
(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 20 5 0x x y x y y
2 225y x5d
,0x
(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 20 5 0x x y x y y
2 225y x
5y x
5d
,0x
(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 20 5 0x x y x y y
2 225y 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
(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 20 5 0x x y x y y
2 225y 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
(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 20 5 0x x y x y y
2 225y 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
(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 20 5 0x x y x y y
2 225y 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
(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 20 5 0x x y x y y
2 225y 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
(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 20 5 0x x y x y y
2 225y 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)
(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 20 5 0x x y x y y
2 225y 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
(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 20 5 0x x y x y y
2 225y 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
2required slope
3
(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 20 5 0x x y x y y
2 225y 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
2required slope
3
2
1 33
y x
2
1 33
y x
3 3 2 6
2 3 9 0
y x
x y
OR
2
1 33
y x
3 3 2 6
2 3 9 0
y x
x y
2 2 2 2
1 2 5 4x y x y
OR
2
1 33
y x
3 3 2 6
2 3 9 0
y x
x y
2 2 2 2
1 2 5 4x y x y
2 2 2 22 1 4 4 10 25 8 16x x y y x x y y
OR
2
1 33
y x
3 3 2 6
2 3 9 0
y x
x y
2 2 2 2
1 2 5 4x y x y
2 2 2 22 1 4 4 10 25 8 16x x y y x x y y
8 12 36 0x y
OR
2
1 33
y x
3 3 2 6
2 3 9 0
y x
x y
2 2 2 2
1 2 5 4x y x y
2 2 2 22 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 33
y x
3 3 2 6
2 3 9 0
y x
x y
2 2 2 2
1 2 5 4x y x y
2 2 2 22 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 33
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