Explanation Given: The minor axis is of length 4 and the foci are ( − 5 , 0 ) and ( 5 , 0 ) . Concept: The equation of the ellipse with the centre at origin, vertices at ( ± a , 0 ) , endpoints of the minor axis at ( 0 , ± b ) and foci at ( ± c , 0 ) is written as x 2 a 2 + y 2 b 2 = 1 , where a > b > 0 and c 2 = a 2 − b 2 . Calculation: It is given that the length of minor axis is 4 .and the foci are ( − 5 , 0 ) and ( 5 , 0 ) . Length of minor axis in this case is 2 b as foci are at ( ± 5 , 0 ) , which is of the form ( ± c , 0 ) . Therefore, the value of b is calculated as follows: 2 b = 4 b = 4 2 Divide by 2 b = 2 By comparing the given foci ( ± 5 , 0 ) with the foci ( ± c , 0 ) of the standard form, value of c is obtained as 5. Now the value of a is calculated by using the relation c 2 = a 2 − b 2 . ( 5 ) 2 = a 2 − ( 2 ) 2 Substitute for b and c a 2 = 25 + 4 Apply

A Graphical Approach to College Algebra, Books a la Carte Edition (6th Edition)

6th Edition

ISBN: 9780321900715

Author: John Hornsby, Margaret L. Lial

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 7.2, Problem 34E

To determine

The equation of the ellipse with minor axis of length as 4 and the foci as (−5,0) and (5,0).

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Chapter 7.2, Problem 33E

Chapter 7.2, Problem 35E

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Chapter 7 Solutions

A Graphical Approach to College Algebra, Books a la Carte Edition (6th Edition)

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

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Identify the graph,...Ch. 7 - Prob. 10T Ch. 7 - Prob. 11T Ch. 7 - Prob. 12T Ch. 7 - Prob. 13T Ch. 7 - Prob. 14T Ch. 7 - Prob. 15T Ch. 7 - Prob. 16T

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The equation of the ellipse with minor axis of length as 4 and the foci as ( − 5 , 0 ) and ( 5 , 0 ) .

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The equation of the ellipse with minor axis of length as 4 and the foci as (−5,0) and (5,0).

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Chapter 7 Solutions