3. Parametric Equations and Motion
Parametric equations is the graph of the
ordered pairs (x, y), where:
x = f (t)
y = g (t)
Basically, the x and y coordinates both have their
own functions to define each coordinate.
t is the parameter
4. Example 1 – calc in PAR mode
For the given parameter interval, graph the
parametric equations:
x = t2
– 2, y = 3t
A. -3 ≤ t ≤ 1
B. -2 ≤ t ≤ 3
C. -3 ≤ t ≤ 3
5. Example 2 – Eliminating the parameter
x = 1 – 2t and y = 2 – t
6. Example 3 – Eliminating the parameter
x = t2
- 2 and y = 3t.
7. Example 4 – Eliminating the parameter
Eliminate the parameter for:
x = 2cos(t) and y = 2sin(t).
8. Example 5: Finding parametric equations
(Going from the line to the parametrization)
Find a parametrization of the line through the points
A = (-2, 3) and B = (3, 6)
9. Same thing – one more time
Find a parametrization of the line through the points
A = (4, 5) and B = (-1, 7)
