10.6 Parametric Equations

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10.6 Parametric Equations
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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

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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

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Both Equations graph the same. The Parametric
states how fast to graph

• Given the equation With respect to time
• Rectangular equation Parametric Equations

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Graphing Parameter equations

• Parameter equations

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Graphing Parameter equations

• Parameter equations

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Change to Rectangular Equation

• Parameter equations to
• Rectangular equation

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Change from Parametric to Rectangular

• Parametric Equations

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Change from Parametric to Rectangular

• Parametric Equations

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Change from Parametric to Rectangular

• Parametric Equations

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Change from Parametric to Rectangular

• Parametric Equations

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Change from Parametric to Rectangular

• Parametric Equations

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Change from Parametric to Rectangular

• Parametric Equations

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Change from Parametric to Rectangular

• x h a Cos? y k b Sin?

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Change from Parametric to Rectangular

• x h a Cos? y k b Sin?

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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

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Homework

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

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Homework

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