What are parametric equations used for?

1 Answer
Wataru
Oct 5, 2014

Parametric equations are useful when a position of an object is described in terms of time #t#. Let us look at a couple of example.

Example 1 (2-D)

If a particle moves along a circular path of radius r centered at #(x_0,y_0)#, then its position at time #t# can be described by parametric equations like:

#{(x(t)=x_0+rcost),(y(t)=y_0+rsint):}#

Example 2 (3-D)

If a particle rises along a spiral path of radius r centered along the #z#-axis, then its position at time #t# can be described by parametric equations like:

#{(x(t)=rcost),(y(t)=rsint),(z(t)=t):}#

Parametric equations are useful in these examples since they allow us to describe each coordinate of the position of a particle separately in terms of time.

I hope that this was helpful.

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