Explanation Given: The given equation of an ellipse is, x 2 4 + y 2 1 = 1 Approach: The basic equation for an ellipse with a horizontal major axis which is used is as follows, x 2 a 2 + y 2 b 2 = 1 Here, a and b are constant values. Expression to find vertices is, V = ( ± a , 0 ) Expression to find Foci is, F = ( ± c , 0 ) , here, c 2 = a 2 − b 2 Expression to find Eccentricity ( e ) , e = c a Calculation: Consider the given equation of the ellipse. x 2 4 + y 2 1 = 1 …… ( 1 ) Compare the above equation with the basic equation for an ellipse and find the vertices as follows, a 2 = 4 a = ± 2 And, b 2 = 1 b = ± 1 Find the vertices, V = ( ± a , 0 ) = ( ± 2 , 0 ) Calculate the value of c as follows, To determine b) The lengths of the major and minor axes. To determine c) To sketch: A graph of the given equation of the ellipse.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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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 12E

To determine

a)

To find:

The vertices, foci and eccentricity of the given equation of ellipse.

To determine

b)

The lengths of the major and minor axes.

To determine

c)

To sketch:

A graph of the given equation of the ellipse.

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Chapter 12.2, Problem 11E

Chapter 12.2, Problem 13E

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Chapter 12 Solutions

Algebra and Trigonometry (MindTap Course List)

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 the given equation of ellipse.

Solution Summary: The author explains how to find the vertices, foci, and eccentricity of the given equation of an ellipse.

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a) To find: The vertices, foci and eccentricity of the given equation of ellipse.

b) The lengths of the major and minor axes.

c) To sketch: A graph of the given equation of the ellipse.

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Chapter 12 Solutions

a)

To find:

The vertices, foci and eccentricity of the given equation of ellipse.

b)

The lengths of the major and minor axes.

c)

To sketch:

A graph of the given equation of the ellipse.