11x1 t11 01 locus (2010)

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