(a)
To find: The graph of the parametric equations, initial and terminal points. Also, indicate the direction in which the curve is traced.
(a)
Answer to Problem 12E
The graph of the parametric equations is shown in figure (1), the initial point and terminal point are
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)
If
If
Therefore, the graph of the parametric equations is shown in figure (1), the initial point and terminal point are
(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 12E
The Cartesian equation for a curve that contains the parameterized curve is
Explanation of Solution
Given information: The equations are
Calculation:
Rewrite the parametric equations as
Add the equations
As shown in the graph, the parameterized curve traces all of the ellipse defined by
Therefore, the Cartesian equation for a curve that contains the parameterized curve is
Chapter 1 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Additional Math Textbook Solutions
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Calculus and Its Applications (11th Edition)
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