Concept explainers
(a)
To plot: 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 22E
The graph of the parametric equations is shown in figure (1), there is no initial point and terminal point is
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)
To have an initial point,
If
Therefore, the graph of the parametric equations is shown in figure (1), there is no initial point and terminal point is
(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 22E
The Cartesian equation for a curve that contains the parameterized curve is
Explanation of Solution
Given information: The equations are
Calculation:
Substitute
As shown in the graph, the parameterized curve traces the lower half 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
Additional Math Textbook Solutions
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