Concept explainers
(a)
To find: The graph of the parametric equations, the initial and terminal points. Also, indicate the direction in which the curve is traced.
(a)
Answer to Problem 21E
The graph of the parametric equations is shown in figure (1), there are no initial and terminal points.
Explanation of Solution
Given information: The equations are
Calculation:
Use the following step to graph the parametric equations by graphing calculator.
Step 1: First press the “ON” button graphical calculator.
Step 2: Press the
Step 3: Press
Step 4: Press
Figure (1)
There are no initial and terminal points, since the interval has no beginning or end point and curve is traced in both the directions.
Therefore, the graph of the parametric equations is shown in figure (1), there are no initial and terminal points.
(b)
To find: The Cartesian equation for a curve that contains the parameterized curve and the portion of the graph of the Cartesian equation that is traced by the parameterized curve.
(b)
Answer to Problem 21E
The Cartesian equation for a curve that contains the parameterized curve is
Explanation of Solution
Given information: The equations are
Calculation:
Simplify the equation
As shown in the graph, the parameterized curve traces the portion of the parabola defined by
Therefore, the Cartesian equation for a curve that contains the parameterized curve is
Chapter 1 Solutions
Calculus: Graphical, Numerical, Algebraic
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