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How does the eccentricity determine the type of conic

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 12E Chapter 10.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 12E

Problem 12E

How does the eccentricity determine the type of conic section?

Step-by-Step Solution:

Solution 12E
Step 1:

the eccentricity , denoted e or is a parameter associated with every conic section. It can be thought of as a measure of how much the conic section deviates from being circular.

In particular,

The eccentricity of a circle is zero.

The eccentricity of an ellipse which is not a circle is greater than zero but less than 1.

The eccentricity of a parabola is 1.

The eccentricity of a hyperbola is greater than 1.

The eccentricity of a line  is infinite.

Furthermore, two conic sections are similar (identically shaped) if and only if they have the same eccentricity.

Step 2 of 1

Chapter 10.4, Problem 12E is Solved
Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: conic, determine, eccentricity, section, type. This expansive textbook survival guide covers 112 chapters, and 5248 solutions. Since the solution to 12E from 10.4 chapter was answered, more than 338 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 12E from chapter: 10.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “How does the eccentricity determine the type of conic section?” is broken down into a number of easy to follow steps, and 10 words.

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