1. and Parametric Equations
13.1 Plane curves
and Parametric Equations
Rita Korsunsky

2. Parametric Equations
For example :

3. Example 1
Sketch the graph of a curve with parametrization:
Method 1
Make a Chart and graph 3 -1 y 4 2 1 -2 x t
Method 2
Eliminate the parameter t and graph
The graph is the same as the graph
we got by using method 1.
Arrows on graph show the direction in
which particle traces the curve as t
increases from –1 to 2.

4. Example 2  
t = 0
(1,0)
x2 + y2 = 1 t
t = 2
t = 0
t = 

5. 
t =
t = 0 t=
(1, 0)
(0, -1)
Example 3

6. Example 4 Sketch the graph and indicate the orientation •
0 Start
t = 0
(1, 1)
t = 1
(t, t)
Particle moves from left to right, and
covers only the right hand portion of the parabola.