# 11X1 T12 01 locus

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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

originy

x4

4

Locus

originy

x44

4

Locus

originy

x44

4

4

Locus

originy

x44

4

4

Locus

originy

x44

4

4

Locus

originy

x44

4

4

yxP ,

Locus

originy

x44

4

4

yxP , 400 22 yx

Locus

originy

x44

4

4

yxP , 400 22 yx1622 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 , 221

31 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 , 221

31 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 , 221

31 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 , 221

31 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 , 221

31 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 , 221

31 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 , 221

31 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

x

yxP , 0, y

,0x

x

yxP ,d 0, y5d

,0x

x

yxP ,d 0, y 2 2 2 20 5 0x x y x y y 5d

,0x

x

yxP ,d 0, y 2 2 2 20 5 0x x y x y y 2 225y x5d ,0x

x

yxP ,d 0, y 2 2 2 20 5 0x x y x y y 2 225y x

5y x

5d

,0x

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

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

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

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

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

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)

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

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

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 23, 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

Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47Slide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54Slide Number 55Slide Number 56Slide Number 57Slide Number 58