11 x1 t11 01 locus (2013)
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Transcript of 11 x1 t11 01 locus (2013)
![Page 1: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/1.jpg)
Locus
![Page 2: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/2.jpg)
Locus
The collection of all points whose location is determined by some
stated law.
Locus
![Page 3: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/3.jpg)
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
![Page 4: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/4.jpg)
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
![Page 5: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/5.jpg)
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
![Page 6: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/6.jpg)
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
![Page 7: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/7.jpg)
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
![Page 8: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/8.jpg)
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
![Page 9: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/9.jpg)
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
![Page 10: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/10.jpg)
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
![Page 11: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/11.jpg)
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
![Page 12: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/12.jpg)
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
![Page 13: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/13.jpg)
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
![Page 14: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/14.jpg)
(ii) A point moves so that it is always 5 units away from the y axis
![Page 15: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/15.jpg)
(ii) A point moves so that it is always 5 units away from the y axis
y
x
![Page 16: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/16.jpg)
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,
![Page 17: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/17.jpg)
(ii) A point moves so that it is always 5 units away from the y axis
y
x
yxP ,5 0, y
![Page 18: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/18.jpg)
(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
![Page 19: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/19.jpg)
(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
![Page 20: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/20.jpg)
(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
![Page 21: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/21.jpg)
(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
![Page 22: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/22.jpg)
(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
![Page 23: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/23.jpg)
(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
![Page 24: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/24.jpg)
(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 ,
![Page 25: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/25.jpg)
(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 ,
![Page 26: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/26.jpg)
(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
![Page 27: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/27.jpg)
(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
![Page 28: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/28.jpg)
(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
![Page 29: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/29.jpg)
(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
![Page 30: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/30.jpg)
(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
![Page 31: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/31.jpg)
(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
![Page 32: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/32.jpg)
(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
![Page 33: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/33.jpg)
(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.
![Page 34: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/34.jpg)
(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
![Page 35: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/35.jpg)
(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 ,
![Page 36: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/36.jpg)
(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
![Page 37: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/37.jpg)
(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
![Page 38: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/38.jpg)
(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
![Page 39: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/39.jpg)
(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
![Page 40: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/40.jpg)
(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
![Page 41: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/41.jpg)
(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
![Page 42: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/42.jpg)
(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
![Page 43: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/43.jpg)
(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
![Page 44: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/44.jpg)
(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
![Page 45: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/45.jpg)
(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
![Page 46: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/46.jpg)
(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
![Page 47: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/47.jpg)
(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)
![Page 48: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/48.jpg)
(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
![Page 49: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/49.jpg)
(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
![Page 50: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/50.jpg)
(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
![Page 51: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/51.jpg)
2
1 33
y x
![Page 52: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/52.jpg)
2
1 33
y x
3 3 2 6
2 3 9 0
y x
x y
![Page 53: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/53.jpg)
OR
2
1 33
y x
3 3 2 6
2 3 9 0
y x
x y
![Page 54: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/54.jpg)
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
![Page 55: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/55.jpg)
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
![Page 56: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/56.jpg)
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
![Page 57: 11 x1 t11 01 locus (2013)](https://reader030.fdocuments.in/reader030/viewer/2022032716/55b601d6bb61eb350a8b46e6/html5/thumbnails/57.jpg)
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
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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