(a)
To evaluate: The graph of the parametric equations, initial and terminal points. Also, indicate the direction in which the curve is traced.
(a)
Answer to Problem 45E
The graph of the parametric equations is shown in figure (1), there is no initial and terminal point.
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 2: Press
Step 3: Press
Figure (1)
There are no initial and terminal points because
Therefore, the graph of the parametric equations is shown in figure (1), there is no initial and terminal point.
(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 45E
The Cartesian equation for a curve that contains the parameterized curve is
Explanation of Solution
Given information: The equations are
Calculation:
Subtract the equations
This equation is the graph of a horizontal hyperbola centered at the origin.
The parameterized curve traces the left branch of the hyperbola 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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