Explanation Definition used: Equation of an ellipse with center at ( 0 , 0 ) , and major axis along x-axis: “An equation of the ellipse with center at ( 0 , 0 ) , foci at ( ± c , 0 ) ( 0 , ± c ) , ends of the minor axis at ( 0 , ± b ) and vertices at ( ± a , 0 ) is x 2 a 2 + y 2 b 2 = 1 where a > b > 0 and b 2 = a 2 − c 2 .” Equation of an ellipse with center at ( 0 , 0 ) , and major axis along y-axis: “An equation of the ellipse with center at ( 0 , 0 ) , foci at ( 0 , ± c ) , ends of the minor axis at ( ± b , 0 ) and vertices at ( 0 , ± a ) is x 2 b 2 + y 2 a 2 = 1 where a > b > 0 and b 2 = a 2 − c 2 .” Calculation: The given equation of the ellipse is x 2 4 + y 2 = 1 . Convert the equation of the ellipse x 2 4 + y 2 = 1 into standard form as follows. x 2 4 + y 2 1 = 1 x 2 2 2 + y 2 1 2 = 1 Clearly, the equation x 2 2 2 + y 2 1 2 = 1 is in the form of x 2 a 2 + y 2 b 2 = 1

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

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 21.5, Problem 3E

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The vertices and the foci of the ellipse with the equation x24+y2=1 and to draw the graph of the ellipse.

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Chapter 21.5, Problem 2E

Chapter 21.5, Problem 4E

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Chapter 21 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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The vertices and the foci of the ellipse with the equation x 2 4 + y 2 = 1 and to draw the graph of the ellipse.

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The vertices and the foci of the ellipse with the equation x24+y2=1 and to draw the graph of the ellipse.

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Chapter 21 Solutions