
Concept explainers
(a)
To explain: The meaning of a parametric curve.
(a)

Explanation of Solution
The parametric curve is defined as the set of points
Thus, a parametric curve has two separate functions for x and y coordinates, which are represented in terms of a variable t, called the parameter.
For example, a circle of radius r is defined by the parametric equations
In general, the curve with parametric equations
(b)
To explain: The method to sketch a parametric curve.
(b)

Explanation of Solution
In general, it is difficult to sketch a parametric curve that is represented by two functions.
Thus, find the values of
Sometimes, the parameter t are eliminated from
That is, it is easier to graph the equation, than working with the original formulas of x and y in terms of t.
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Chapter 9 Solutions
Essential Calculus: Early Transcendentals
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