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Chapter 10: Q. 5. (page 694)

True or False Parametric equations defining a curve are unique.

Short Answer

Expert verified

The answer is false.

Step by step solution

01

Step 1. Given information.

A curve and parametric equations.

02

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=2sin(t),y=3cos(t) and x=3sin(t),y=4cos(t)

both parametric equations represent the curve of an ellipse.

Hence, Parametric equations defining a curve are unique is false

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