1. Date Calculus AB Ms. Brewer
1.4 Parametric Equations
Date
Calculus AB
Ms. Brewer

2. Vocab/Formulas Relation: set of ordered pairs (x,y) of real numbers.
If x and y are functions of t (the parameter), you can use parametric mode in a calculator.

3. Example 1: Graph the half parabola using the parametric equations.
t x y
Initial Point:
Terminal Point:
Direction in which curve is traced:
Your calculator can only draw a parametric curve in a closed interval even when the curve has no endpoints!

4. Example 1: Find a Cartesian equation for the curve.

5. Vocab/Formulas
Parametric Curve and Equations: If x and y are given as functions
over an interval of t-values, then the set of points (x,y)=(f(t),g(t)) defined by these equations is a parametric curve. The equations are parametric equations.
Parameter: t when a ≤ t ≤ b
Parameter Interval

6. Parameterizing Circles and Ellipses

7. Example 2: Graph the parametric curve

8. Example 3: Draw and identify the graph of the parametric curve determined by:

9. Example 3: Confirm algebraically that this is a line.

10. Example 4: Graph the “Witch of Agnesi”
Example 4: Graph the “Witch of Agnesi”. See the history of Maria Gaetana Agnesi on pg. 33

11. Example 5: Find a parameterization for the line segment with endpoints (-2,1) and (3,5)

12. Assignment
Pg , 9, 13, 17, 19, 21, 23, 25