1. Parametric Coordinates

2. Parametric Coordinates
Cartesian Coordinates: curve is described by one equation and points
are described by two numbers.

3. 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).

4. 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

5. 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

6. 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

7. 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

8. 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
2
2 ,x at y at 

9. 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
2
2 ,x at y at  Parametric coordinates

10. 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
2
2 ,x at y at  Parametric coordinates
(2 , )a a

11. 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
2
2 ,x at y at  Parametric coordinates
(2 , )a a Cartesian coordinates

12. 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
2
2 ,x at y at  Parametric coordinates
(2 , )a a Cartesian coordinates
1t 

13. 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
2
2 ,x at y at  Parametric coordinates
(2 , )a a Cartesian coordinates
1t  parameter

14. 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
2
2 ,x at y at  Parametric coordinates
(2 , )a a Cartesian coordinates
1t  parameter
( 4 ,4 )a a
2t  

15. 2
4x ayAny point on the parabola has coordinates;

16. 2
4x ay
2x at
Any point on the parabola has coordinates;

17. 2
4x ay
2x at 2
y at
Any point on the parabola has coordinates;

18. 2
4x ay
2x at 2
y at
Any point on the parabola has coordinates;
where; a is the focal length

19. 2
4x ay
2x at 2
y at
Any point on the parabola has coordinates;
where; a is the focal length
t is any real number

20. 2
4x ay
2x at 2
y 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 4
x t y t 

21. 2
4x ay
2x at 2
y 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 4
x t y t 
2t x

22. 2
4x ay
2x at 2
y 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 4
x t y t 
2t x  
21
2
4
y x

23. 2
4x ay
2x at 2
y 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 4
x t y t 
2t x  
21
2
4
y x
 2
2
1
4
4
y x
y x



24. 2
4x ay
2x at 2
y 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 4
x t y t 
2t x  
21
2
4
y x
 2
2
1
4
4
y x
y x


(ii) State the coordinates of the focus

25. 2
4x ay
2x at 2
y 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 4
x t y t 
2t x  
21
2
4
y x
 2
2
1
4
4
y x
y x


(ii) State the coordinates of the focus
1
4
a 

26. 2
4x ay
2x at 2
y 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 4
x t y t 
2t x  
21
2
4
y x
 2
2
1
4
4
y x
y x


(ii) State the coordinates of the focus
1
4
a 
1
focus 0,
4
 
   
 

27. (iii) Calculate the parametric coordinates of the curve 2
8y x

28. (iii) Calculate the parametric coordinates of the curve 2
8y x
2
4x ay

29. (iii) Calculate the parametric coordinates of the curve 2
8y x
2
4x ay
1
4
8
1
32
a
a



30. (iii) Calculate the parametric coordinates of the curve 2
8y x
2
4x ay
1
4
8
1
32
a
a


21 1
the parametric coordinates are ,
16 32
t t
 
  
 

31. (iii) Calculate the parametric coordinates of the curve 2
8y x
2
4x ay
1
4
8
1
32
a
a


21 1
the parametric coordinates are ,
16 32
t t
 
  
 
Exercise 9D; 1, 2 (not latus rectum), 3, 5, 7a