MTH 251 Lecture Notes - Lecture 33: Parametric Equation

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Section  : Parametric equations
Suppose an ant traces out a path on a flat surface
Suppose the curve is something like:
This curve is neither a function of nor
But both and are functions of ; we can write    
So, for a given  we have the point    
These are called parametric equations, as varies,   traces out the curve.
Example: Sketch     
No restriction no here.





We can eliminate the parameter :
  
So,    
Sometime, can be restricted:
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