Explanation Given: The equation of a hyperbola is x 2 + 4 y 2 = 1 Approach: For an ellipse with horizontal major axis x 2 a 2 + y 2 b 2 = 1 , a > 0 , b > 0 The vertices are ( ± a , 0 ) . The foci are ( ± c , 0 ) , c 2 = a 2 − b 2 The eccentricity is e = c a Calculation: The standard form of given hyperbola is x 2 2 2 + y 2 ( 2 ) 2 = 1 This gives a = 2 , b = 2 . To determine (b) To find: The length of major and minor axis of an ellipse To determine (c) To sketch: The graph of an ellipse

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ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Chapter 12.2, Problem 27E

To determine

(a)

To find:

The vertices, foci and eccentricity of an ellipse

To determine

(b)

To find:

The length of major and minor axis of an ellipse

To determine

(c)

To sketch:

The graph of an ellipse

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Chapter 12.2, Problem 26E

Chapter 12.2, Problem 28E

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Chapter 12 Solutions

Algebra and Trigonometry

Ch. 12.1 - A parabola is the set of all points in the plane...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 8E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 10E

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(a) To find: The vertices, foci and eccentricity of an ellipse

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(a) To find: The vertices, foci and eccentricity of an ellipse

(b) To find: The length of major and minor axis of an ellipse

(c) To sketch: The graph of an ellipse

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Chapter 12 Solutions

(a)

To find:

The vertices, foci and eccentricity of an ellipse

(b)

To find:

The length of major and minor axis of an ellipse

(c)

To sketch:

The graph of an ellipse