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