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 4ay
x
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 4ay Cartesian equation
x
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 4ay Cartesian equation
x 2at , y at 2
x
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 4ay Cartesian equation
x 2at , y at 2 Parametric coordinates
x
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 4ay Cartesian equation
x 2at , y at 2 Parametric coordinates
(2a, a)
x
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 4ay Cartesian equation
x 2at , y at 2 Parametric coordinates
(2a, a) Cartesian coordinates
x
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 4ay Cartesian equation
x 2at , y at 2 Parametric coordinates
(2a, a) Cartesian coordinates
t 1
x
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 4ay Cartesian equation
x 2at , y at 2 Parametric coordinates
(2a, a) Cartesian coordinates
t 1 parameter
x
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 4ay Cartesian equation
(4a, 4a) x 2at , y at 2 Parametric coordinates
t 2
(2a, a) Cartesian coordinates
t 1 parameter
x
15. Any point on the parabola x 2 4ay has coordinates;
16. Any point on the parabola x 2 4ay has coordinates;
x 2at
17. Any point on the parabola x 2 4ay has coordinates;
x 2at y at 2
18. Any point on the parabola x 2 4ay has coordinates;
x 2at y at 2
where; a is the focal length
19. Any point on the parabola x 2 4ay has coordinates;
x 2at y at 2
where; a is the focal length
t is any real number
20. Any point on the parabola x 2 4ay has coordinates;
x 2at y at 2
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
1 1
x t , y t2
2 4
21. Any point on the parabola x 2 4ay has coordinates;
x 2at y at 2
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
1 1
x t , y t2
2 4
t 2x
22. Any point on the parabola x 2 4ay has coordinates;
x 2at y at 2
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
1 1
x t , y t2
2 4
1
y 2x
2
t 2x
4
23. Any point on the parabola x 2 4ay has coordinates;
x 2at y at 2
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
1 1
x t , y t2
2 4
1
y 2x
2
t 2x
4
y 4x2
1
4
y x2
24. Any point on the parabola x 2 4ay has coordinates;
x 2at y at 2
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
1 1
x t , y t2
2 4
1
y 2x
2
t 2x
4
y 4x2
1
4
y x2
(ii) State the coordinates of the focus
25. Any point on the parabola x 2 4ay has coordinates;
x 2at y at 2
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
1 1
x t , y t2
2 4
1
y 2x
2
t 2x
4
y 4x2
1
4
y x2
(ii) State the coordinates of the focus
1
a
4
26. Any point on the parabola x 2 4ay has coordinates;
x 2at y at 2
where; a is the focal length
t is any real number
e.g. Eliminate the parameter to find the cartesian equation of;
1 1
x t , y t2
2 4
1
y 2x
2
t 2x
4
y 4x2
1
4
y x2
(ii) State the coordinates of the focus 1
a
1 focus 0,
4 4
29. (iii) Calculate the parametric coordinates of the curve y 8 x 2
x 2 4ay
1
4a
8
1
a
32
30. (iii) Calculate the parametric coordinates of the curve y 8 x 2
x 2 4ay
1
4a
8
1
a
32
1 1
the parametric coordinates are t , t 2
16 32
31. (iii) Calculate the parametric coordinates of the curve y 8 x 2
x 2 4ay
1
4a
8
1
a
32
1 1
the parametric coordinates are t , t 2
16 32
Exercise 9D; 1, 2 (not latus rectum), 3, 5, 7a