Thursday, June 30, 2011

Parametric

A pair or a set of parametric equations may look like
,
or
,
or
,
or
.


See the common feature?


Now, let's try to combine the variables:
a)


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This is a vertical line x=2.


b)


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This is a vertical ellipse centered at the origin with vertices at (0,3) and (0,-3), and endpoints of minor axis at (2,0) and (-2,0).


c)


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This is a sine function with magnitude 2.


d)
This is an object in 3-dimension.


You see, parametric equations can form a lot of curve with different type:
a) function, non-function;
b) line, curve;
c) 2-D, 3-D;
etc.

Can you try to build one set of parametric equations and figure out the graph of the set of equations?

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