MA 141 Lecture 4: Parametric CurvesExam
Course CodeMA 141
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MA 141 Chapter 0
Section 0.4: Parametric Curves
We have discussed several diﬀerent types of functions. What do we do with those curves that
are not functions? It turns out that we can describe such curves using a pair of functions,
one for each variable.
Def: Let f(t)and g(t)be two functions deﬁned on the interval t∈[a, b]. Then the curve in
the xy-plane given by
(x, y) = (f(t), g(t)) , t ∈[a, b]
is called a parametric curve, and tis the parameter along the curve.
Given a parametric curve with x=f(t)and y=g(t), we can solve both equations for tand
set them equal to each other or substitute one into the other. This will give us the usual
Cartesian equation in only xand y.
Ex: Let x=t+ 1 and y=t2. Find the Cartesian equation (eliminate the parameter t).
If x=t+ 1, then t=x−1. Then
This is a vertical parabola centered at (1,0).
Ex: Graph the parametric curve given by x= 4 cos tand y= 3 sin tfor t∈[0,2π). Then
ﬁnd the Cartesian equation.
To graph this, use a table and choose a selection of tvalues:
t x y
0 4 0
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