Concept explainers
(a)
To find: The length of the string in terms of
(a)
Answer to Problem 69E
The length of the string in terms of
Explanation of Solution
Given information:
An ellipse can be drawn using two thumbtacks, a string of fixed length and a pencil. When the ends of the string are fastened, all the tacks and the string is drawn taut with a pencil. The path traced by the pencil is ellipse.
Calculation:
Assume that two thumbtacks are the foci of any ellipse and represented by
From figure, center of foci is
So,
Calculate the length of the string
Therefore, the length of the string in terms of
(b)
To explain: The reason for path to be an elliptical curve.
(b)
Answer to Problem 69E
The path traced by pencil is elliptical.
Explanation of Solution
Given information:
An ellipse can be drawn using two thumbtacks, a string of fixed length and a pencil. When the ends of the string are fastened all the tacks and the string is drawn taut with a pencil, the path traced by the pencil is ellipse.
The given activity satisfies the definition of an ellipse that is an ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant.
Therefore, the path traced by pencil is elliptical.
Chapter 9 Solutions
Precalculus with Limits: A Graphing Approach
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning