ELIMINATING THE PARAMETER IN PARAMETRIC EQUATIONS

Let x and y represent functions of the same variable, t, called the parameter, defined on some specified intervals of t-values. The functions x(t) and y(t) are the parametric equations. In this section, we are going to see, how to eliminate the parameter and write the equation in terms of the variables x and y.

Problem 1 :

(a) Eliminate the parameter from

x = 3t

y = t2 + 1

(b) Sketch the graph of that curve for parameter values

-1 t ≤ 3

Indicate the orientation of the curve.

Solution :

Problem 2 :

(a) Eliminate the parameter from

x = 4cosθ

y = 9sinθ

(b) Sketch the graph of that curve for parameter values

≤ θ ≤ π

Indicate the orientation of the curve.

Solution :

Problem 3 :

Eliminate the parameter in the parametric equations :

x = cosh t

y = sinh t

Solution :

Problem 4 :

Eliminate the parameter in the parametric equations :

x = sin t

y = cos 2t

Solution :

Problem 5 :

(a) Eliminate the parameter from

x = 3t

y = t2 - 1

(b) Sketch the graph of that curve for parameter values

t ≤ 2

Indicate the orientation of the curve.

Solution :

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