This document discusses parametric equations and motion. It provides examples of parametrizing lines and circles using parametric equations with a parameter t. It gives two examples each of graphing parametric equations for a given parameter interval, eliminating the parameter to get a standard equation, and finding the parametric equations of a line given two points. It assigns homework problems from the textbook on these topics involving parametric equations.

1. Homework Questions…

2. Pre-Calculus
Section 6.3 in your book…

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)

10. Find the parametrization
 A circle with center at (1, 3) and radius 7.

11. Homework!
 p. 530 (1-4, 20-32 even)