11X1 T12 01 locus

Locus

LocusThe collection of all points whose location is determined by some stated law.

Locus

LocusThe 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

LocusThe 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

originy

x

Locus

LocusThe 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

originy

x4

Locus

LocusThe 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

originy

x4

4

Locus

LocusThe 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

originy

x4–4

4

Locus

LocusThe 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

originy

x4–4

4

–4

Locus

LocusThe 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

originy

x4–4

4

–4

Locus

LocusThe 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

originy

x4–4

4

–4

Locus

LocusThe 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

originy

x4–4

4

–4

yxP ,

Locus

LocusThe 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

originy

x4–4

4

–4

yxP , 400 22 yx

Locus

LocusThe 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

originy

x4–4

4

–4

yxP , 400 22 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 axisy

x

(ii) A point moves so that it is always 5 units away from the y axisy

x

yxP ,

(ii) A point moves so that it is always 5 units away from the y axisy

x

yxP ,5 0, y

(ii) A point moves so that it is always 5 units away from the y axisy

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 axisy

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 axisy

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 axisy

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 axisy

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 axisy

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 axisy

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 axisy

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 axisy

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 axisy

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 axisy

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 axisy

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 axisy

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 axisy

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 axisy

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, y5d

,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 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

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 25 16

43

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 25 16

43

2

ABm

2required slope3

(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 25 16

43

2

ABm

1 5 4 2,2 2

3, 1

ABM

2required slope3

21 33

y x

21 33

y x

3 3 2 62 3 9 0y xx y

OR

21 33

y x

3 3 2 62 3 9 0y xx y

2 2 2 21 2 5 4x y x y

OR

21 33

y x

3 3 2 62 3 9 0y xx y

2 2 2 21 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

21 33

y x

3 3 2 62 3 9 0y xx y

2 2 2 21 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

21 33

y x

3 3 2 62 3 9 0y xx y

2 2 2 21 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

21 33

y x

3 3 2 62 3 9 0y xx y

2 2 2 21 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

21 33

y x

3 3 2 62 3 9 0y xx y

Exercise 9A; 1aceg, 3a, 4, 6, 8, 10, 11, 13, 14