11X1 T12 03 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

y x 2  4ay

x

y x 2  4ay Cartesian equation

x

x  2at , y  at 2

x

x  2at , y  at 2 Parametric coordinates

x


(2a, a )

x


(2a, a ) Cartesian coordinates

x


t 1
x


t 1 parameter
x

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

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


x  2at


x  2at y  at 2


x  2at y  at 2

where; a is the focal length


x  2at y  at 2

t is any real number


x  2at y  at 2


e.g. Eliminate the parameter to find the cartesian equation of;
1 1
x  t , y  t2
2 4


x  2at y  at 2


1 1
x  t , y  t2
2 4
t  2x


x  2at y  at 2


1 1
x  t , y  t2
2 4
1
y   2x
2
t  2x
4


x  2at y  at 2


1 1
x  t , y  t2
2 4
1
y   2x
2
t  2x
4
y   4x2 
1
4
y  x2


x  2at y  at 2


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


x  2at y  at 2


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


x  2at y  at 2


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

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

x 2  4ay

x 2  4ay
1
4a 
8
1
a
32

x 2  4ay
1
4a 
8
1
a
32
 the parametric coordinates are  t , t 2 
1 1
 
 16 32 

x 2  4ay
1
4a 
8
1
a
32
 the parametric coordinates are  t , t 2 
1 1
 
 16 32 

Exercise 9D; 1, 2 (not latus rectum), 3, 5, 7a

11X1 T12 03 parametric coordinates

More Related Content

What's hot (18)

Similar to 11X1 T12 03 parametric coordinates (20)

More from Nigel Simmons (20)

Recently uploaded (20)

11X1 T12 03 parametric coordinates