Question

True or False Parametric equations defining a curve are unique.

Short answer

The answer is false.

Step-by-step solution

Step 1. Given information.

A curve and parametric equations.

Step 2. Calculation.

Parametric equations defining a curve are unique is false because parameterizations are non-unique, more than one set of parametric equations can specify the same curve.

For example, $x=2\sin \left(t\right),y=3\cos \left(t\right)$ and $x=3\sin \left(t\right),y=4\cos \left(t\right)$

both parametric equations represent the curve of an ellipse.

Hence, Parametric equations defining a curve are unique is false