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10.6 Parametric Equations

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10.6 Parametric Equations Definition of Parametric Equations parametric equation is a method of defining a relation using parameters. A simple kinematic1 example is ... – PowerPoint PPT presentation

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Title: 10.6 Parametric Equations


1
10.6 Parametric Equations
2
Definition of Parametric Equations
  • parametric equation is a method of defining a
    relation using parameters. A simple kinematic1
    example is when one uses a time parameter to
    determine the position, velocity, and other
    information about a body in motion.
  • 1. Kinematic.The branch of mechanics that studies
    the motion of a body or a system of bodies
    without consideration given to its mass or the
    forces acting on it.
  • http//en.wikipedia.org/wiki/Parametr
    ic_equation

3
We will not be finding parametric equations, in
this example.
  • In this class we will graph parametric equation
    also eliminating the parameter.
  • Given the equation With respect to time
  • Rectangular equation Parametric Equations
  • The parametric equations have to be
    Continuous

4
Both Equations graph the same. The Parametric
states how fast to graph
  • Given the equation With respect to time
  • Rectangular equation Parametric Equations

5
Graphing Parameter equations
  • Parameter equations

6
Graphing Parameter equations
  • Parameter equations

7
Change to Rectangular Equation
  • Parameter equations to
  • Rectangular equation

8
Change from Parametric to Rectangular
  • Parametric Equations

9
Change from Parametric to Rectangular
  • Parametric Equations

10
Change from Parametric to Rectangular
  • Parametric Equations

11
Change from Parametric to Rectangular
  • Parametric Equations

12
Change from Parametric to Rectangular
  • Parametric Equations

13
Change from Parametric to Rectangular
  • Parametric Equations

14
Change from Parametric to Rectangular
  • x h a Cos? y k b Sin?

15
Change from Parametric to Rectangular
  • x h a Cos? y k b Sin?

16
What would the parametric equation be for a
circle with center at (3,2) and radius of 4
  • (x h)2 (y k)2 r2 In a circle a b 4

17
Homework
  • Page 747 749
  • 7, 14, 21, 28,
  • 32, 41, 48

18
Homework
  • Page 747 749
  • 5, 10, 15, 20,
  • 25, 30, 35, 40
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