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There are many ways to describe a curve. Consider the following descriptions:

• the unit circle;
• $x^2+y^2=1$;
• $y=\sqrt{1-x^2}$;
• $r=1$;
• $x=\cos\phi$, $y=\sin\phi$;
• $\rr(\phi)=\cos\phi\,\xhat+\sin\phi\,\yhat$;

all of which describe (pieces of) the same curve. Here are some more:

• The graph of $y=x^2$;
• The figure shown at the right.

Which representation is best for a given problem depends on the circumstances.