(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 8E
The graph of the parametric equations with the direction is shown in Figure (1), there are no initial or 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 2: Press
Step 3: Press
Figure (1)
From the graph it can be seen that there are no initial or terminal points.
Therefore, the graph of the parametric equations with the direction is shown in Figure (1), there are no initial or terminal points.
(b)
To find: The Cartesian equation and the portion of the graph of the Cartesian equation that is traced by the parameterized curve.
(b)
Answer to Problem 8E
The Cartesian equation is
Explanation of Solution
Given information: The equations are
Calculation:
Simplify the equation
Square both sides of the equation
Substitute
The above Cartesian form is an equation of parabola. From the graph shown in part (a), the entire portion of the graph is traced by parameterized curve.
Therefore, the Cartesian equation is
Chapter 1 Solutions
Calculus: Graphical, Numerical, Algebraic
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