Parametric Coordinates
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Parametric Coordinates
Parametric CoordinatesCartesian Coordinates: curve is described by one equation and points
are described by two numbers.
Parametric CoordinatesCartesian 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 CoordinatesCartesian 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 CoordinatesCartesian 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 CoordinatesCartesian 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 CoordinatesCartesian 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 CoordinatesCartesian 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 equation22 , x at y at
Parametric CoordinatesCartesian 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 equation22 , x at y at Parametric coordinates
Parametric CoordinatesCartesian 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 equation22 , x at y at Parametric coordinates
(2 , )a a
Parametric CoordinatesCartesian 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 equation22 , x at y at Parametric coordinates
(2 , )a a Cartesian coordinates
Parametric CoordinatesCartesian 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 equation22 , x at y at Parametric coordinates
(2 , )a a Cartesian coordinates1t
Parametric CoordinatesCartesian 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 equation22 , x at y at Parametric coordinates
(2 , )a a Cartesian coordinates1t parameter
Parametric CoordinatesCartesian 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 equation22 , x at y at Parametric coordinates
(2 , )a a Cartesian coordinates1t 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 at 2y at
Any point on the parabola has coordinates;
2 4x ay
2x at 2y at
Any point on the parabola has coordinates;
where; a is the focal length
2 4x ay
2x at 2y at
Any point on the parabola has coordinates;
where; a is the focal lengtht is any real number
2 4x ay
2x at 2y at
Any point on the parabola has coordinates;
where; a is the focal lengtht 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 at 2y at
Any point on the parabola has coordinates;
where; a is the focal lengtht 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 at 2y at
Any point on the parabola has coordinates;
where; a is the focal lengtht 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 at 2y at
Any point on the parabola has coordinates;
where; a is the focal lengtht 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
1 44
y x
y x
2 4x ay
2x at 2y at
Any point on the parabola has coordinates;
where; a is the focal lengtht 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
1 44
y x
y x
(ii) State the coordinates of the focus
2 4x ay
2x at 2y at
Any point on the parabola has coordinates;
where; a is the focal lengtht 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
1 44
y x
y x
(ii) State the coordinates of the focus
14
a
2 4x ay
2x at 2y at
Any point on the parabola has coordinates;
where; a is the focal lengtht 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
1 44
y x
y x
(ii) State the coordinates of the focus
14
a 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
148132
a
a
(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay
148132
a
a
21 1 the parametric coordinates are ,16 32
t t
(iii) Calculate the parametric coordinates of the curve 28y x2 4x ay
148132
a
a
21 1 the parametric coordinates are ,16 32
t t
Exercise 9D; 1, 2 (not latus rectum), 3, 5, 7a
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