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 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
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