11 x1 t11 03 parametric coordinates (2012)
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Parametric Coordinates
Parametric Coordinates Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.
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).
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
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
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
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
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 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
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
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
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
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
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
2 4x ayAny point on the parabola has coordinates;
2 4x ay
2x at
Any point on the parabola has coordinates;
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
2 4x ay
2x at2y at
Any point on the parabola has coordinates;
where; a is the focal length
t is any real number
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
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
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 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
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
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
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
(iii) Calculate the parametric coordinates of the curve 28y x
(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay
(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay
14
8
1
32
a
a
(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
(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
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