Answer
False
Work Step by Step
Parametric equations defining a curve are NOT unique. For example, the following sets of equations define the same curve:
$\begin{cases}
x=\cos t\\
y=\sin t
\end{cases}$
$\begin{cases}
x=\sin t\\
y=\cos t
\end{cases}$
The curve is:
$x^2+y^2=1$
Therefore the given statement is FALSE.
