Parametric equations worksheet
Brian_1234
parametriceqn_034.docParametric Equations 8.5 NAME____________________
Parametric equations are a general method for describing any curve.
There are three variables for each “point”, the x direction, the y direction and t, the time it takes to get to that point.
1. Given the equations
t
x
=
4
yt
=-+
a. Fill in the following table and graph the points. Indicate the direction of the curve/line with respect to time by using arrows.
|
T |
x |
y |
|
0 |
0 |
4 |
|
1 |
1 |
3 |
|
2 |
1.41 |
2 |
|
3 |
1.73 |
1 |
|
4 |
2 |
0 |
Soln:
b. Using the two original equations, eliminate the parameter, t, to obtain an equation for y as a function of x. Does the equation you found match the function you’ve drawn?
Soln:
Take the any x, y points =(1,3)
Find the slop of the point is
1
2
1
2
x
x
y
y
m
-
-
=
3
1
3
1
2
3
0
-
=
-
=
-
-
=
m
m
m
using another points to find the slope its available so take the point (2,0)
Equation is
b
mx
y
+
=
3
,
1
=
=
y
x
6
3
3
1
3
3
=
+
=
+
´
-
=
b
b
b
Standard equation is
6
3
+
-
=
x
y
2. Find the parametric equations x(t) & y(t) for the line that passes through the point (3,6) , when t=0 and (-4, 9), when t = 2. *hint substitute in t & x, t & y for point 1& 2 then solve for a, b, c, d
x(t) = a +bt
y(t) = c + dt
Soln:
a=3
b=6
c=-4
d=9
3. Sketch a graph of
sin()
cos(2)
xt
yt
=
=
and write it as a Cartesian equation
Soln:
4. Sketch a graph of
sin(2)
cos()
xt
yt
=
=
and write it as a Cartesian equation
Soln:
X
Y
