Concept explainers
(a)
Write the area of the ellipse as a function of
(a)
Answer to Problem 67E
Area=
Explanation of Solution
Given:
The general form of the ellipse as
Also,
The area of the ellipse is given as
To express the area in terms of the variable a.
From equation (1)
Substituting the value of B in the expression for area,
Area=
(b)
Find the equation of an ellipse with an area of 264 square centimeters.
(b)
Answer to Problem 67E
The general equation,
Explanation of Solution
Given:
To find the equation of an ellipse with an area of 264 square centimeters.
Substituting this value in the expression for area,
This gives
Also,
Substituting the values of a and b in the general equation,
(c)
Complete the table using your equation from part (a). Then make a conjecture about the shape of the ellipse with maximum area.
(c)
Answer to Problem 67E
| 8 | 9 | 10 | 11 | 12 | 13 |
A | 301.6 | 311.0 | 314.2 | 311.0 | 301.6 | 285.9 |
Explanation of Solution
Given:
| 8 | 9 | 10 | 11 | 12 | 13 |
A | 301.6 | 311.0 | 314.2 | 311.0 | 301.6 | 285.9 |
The various values of a are given.
From the above table the maximum area occurs at NA=10
In this case, both a and b turn out to be 10.
Thus, a circle has maximum area.
(d)
To graph the area function using a graphing utility.
(d)
Answer to Problem 67E
Graph is shown below.
The peak of the curve occurs at
Explanation of Solution
Given:
The area function is given as
The area function is given as
The graph comes out to be
The peak of the curve occurs at
Chapter 10 Solutions
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