11 x1 t11 03 parametric coordinates (2012)
TRANSCRIPT
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Parametric Coordinates
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Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
![Page 3: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/3.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
![Page 4: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/4.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
![Page 5: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/5.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
![Page 6: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/6.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
2 4x ay
![Page 7: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/7.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
2 4x ay Cartesian equation
![Page 8: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/8.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
2 4x ay Cartesian equation 22 , x at y at
![Page 9: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/9.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
2 4x ay Cartesian equation 22 , x at y at Parametric coordinates
![Page 10: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/10.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
2 4x ay Cartesian equation 22 , x at y at Parametric coordinates
(2 , )a a
![Page 11: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/11.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
2 4x ay Cartesian equation 22 , x at y at Parametric coordinates
(2 , )a a Cartesian coordinates
![Page 12: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/12.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
2 4x ay Cartesian equation 22 , x at y at Parametric coordinates
(2 , )a a Cartesian coordinates 1t
![Page 13: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/13.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
2 4x ay Cartesian equation 22 , x at y at Parametric coordinates
(2 , )a a Cartesian coordinates 1t parameter
![Page 14: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/14.jpg)
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric Coordinates: curve is described by two equations and points
are described by one number (parameter).
y
x
2 4x ay Cartesian equation 22 , x at y at Parametric coordinates
(2 , )a a Cartesian coordinates 1t parameter
( 4 ,4 )a a2t
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2 4x ayAny point on the parabola has coordinates;
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2 4x ay
2x at
Any point on the parabola has coordinates;
![Page 17: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/17.jpg)
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
![Page 18: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/18.jpg)
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
![Page 19: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/19.jpg)
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
t is any real number
![Page 20: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/20.jpg)
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
21 1 ,
2 4x t y t
![Page 21: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/21.jpg)
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
21 1 ,
2 4x t y t
2t x
![Page 22: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/22.jpg)
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
21 1 ,
2 4x t y t
2t x 21
24
y x
![Page 23: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/23.jpg)
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
21 1 ,
2 4x t y t
2t x 21
24
y x
2
2
14
4y x
y x
![Page 24: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/24.jpg)
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
21 1 ,
2 4x t y t
2t x 21
24
y x
2
2
14
4y x
y x
(ii) State the coordinates of the focus
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2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
21 1 ,
2 4x t y t
2t x 21
24
y x
2
2
14
4y x
y x
(ii) State the coordinates of the focus 1
4a
![Page 26: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/26.jpg)
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
21 1 ,
2 4x t y t
2t x 21
24
y x
2
2
14
4y x
y x
(ii) State the coordinates of the focus 1
4a
1 focus 0,
4
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(iii) Calculate the parametric coordinates of the curve 28y x
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(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay
![Page 29: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/29.jpg)
(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay
14
8
1
32
a
a
![Page 30: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/30.jpg)
(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay
14
8
1
32
a
a
21 1 the parametric coordinates are ,
16 32t t
![Page 31: 11 x1 t11 03 parametric coordinates (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052901/556f5e6bd8b42a916b8b510e/html5/thumbnails/31.jpg)
(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay
14
8
1
32
a
a
21 1 the parametric coordinates are ,
16 32t t
Exercise 9D; 1, 2 (not latus rectum), 3, 5, 7a