Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

A hyperbola for which $a = b$ is called an equilateral hyperbola. Find the eccentricity $e$ of an equilateral hyperbola.
[Note: The eccentricity of a hyperbola is defined in Problem 81.]

The eccentricity of a equilateral hyperbola is $\sqrt{2}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Eccentricity

Eccentricity is a number that is calculate in the following way

$e = \frac{c}{a}$

where $a$ is the distance from the center to the vertex and $c$ is the distance from the center to the focus.

Finding the eccentricity

For an equilateral hyperbola, it hold that $a = b$

For any hyperbola the following formula holds:

$b^{2} = c^{2} - a^{2}$

therefore

$c^{2} = a^{2} + b^{2}$

Since, $a = b$ , you can write previous equation as

$c^{2} = a^{2} + a^{2} = 2 a^{2}$

then

$c = a \sqrt{2}$

Finding the eccentricity

Put $c = a \sqrt{2}$ in the eccentricity formula to get

$e = \frac{a \sqrt{2}}{a} e = \sqrt{2}$

Step 4. Conclusion

The eccentricity of a equilateral hyperbola is $\sqrt{2}$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

A hyperbola for which $a = b$ is called an equilateral hyperbola. Find the eccentricity $e$ of an equilateral hyperbola.
[Note: The eccentricity of a hyperbola is defined in Problem 81.]

Step by Step Solution

Step 1. Eccentricity

Finding the eccentricity

Finding the eccentricity

Step 4. Conclusion

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

A hyperbola for which a = b is called an equilateral hyperbola. Find the eccentricity e of an equilateral hyperbola. [Note: The eccentricity of a hyperbola is defined in Problem 81.]

Step by Step Solution

Step 1. Eccentricity

Finding the eccentricity

Finding the eccentricity

Step 4. Conclusion

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A hyperbola for which $a = b$ is called an equilateral hyperbola. Find the eccentricity $e$ of an equilateral hyperbola.
[Note: The eccentricity of a hyperbola is defined in Problem 81.]