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 4 x 2 25 + 9 y 2 4 = 1 . Convert the equation of the ellipse 4 x 2 25 + 9 y 2 4 = 1 into standard form as follows. 4 x 2 25 + 9 y 2 4 = 1 x 2 25 4 + y 2 4 9 = 1 x 2 ( 5 2 ) 2 + y 2 ( 2 3 ) 2 = 1 Clearly, the equation x 2 ( 5 2 ) 2 + y 2 ( 2 3 ) 2 = 1 is in the form of x 2 a 2 + y 2 b 2 = 1

11th Edition

ISBN: 9780134437705

Author: Washington

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 7E

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The vertices and the foci of the ellipse with the equation 4x225+9y24=1 and to draw the graph of the ellipse.

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Chapter 21.5, Problem 6E

Chapter 21.5, Problem 8E

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Chapter 21 Solutions

Basic Technical Mathematics

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 4 x 2 25 + 9 y 2 4 = 1 and to draw the graph of the ellipse.

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The vertices and the foci of the ellipse with the equation 4x225+9y24=1 and to draw the graph of the ellipse.

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Chapter 21 Solutions