Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.a. A set of parametric equations for a given curve is always unique.b. The equations x = e?, y = 2e? for ??

Solution 1REStep 1:(a).A set of parametric equations for a given curve is always unique.This statement is false.A curve in the plain is said to be parameterized if the set of coordinates on the curve (x,y) are represented as a function of variable t.Namely , where D is a set of real numbers.The variable t is called a parameter and the relations between x,y and t are called the parametric equations.The D is called the domain of f and g and it is the set of values t takes.Let us consider an example .Consider a parabola Here if we take If we take ie and are parametric equations for the parabola .Thus a set of parametric equations for a given curve is not always unique.