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 .” The distance between two points: The formula for distance between any two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . Calculation: Given that the center is at ( 0 , 0 ) and the sum of the distance from ( x , y ) to ( 6 , 0 ) and ( − 6 , 0 ) is 20. Use the distance formula to obtain the distance between ( x , y ) to ( 6 , 0 ) and ( x , y ) to ( − 6 , 0 ) as follows: d 1 = ( x − 6 ) 2 + ( y − 0 ) 2 d 1 = ( x − 6 ) 2 + y 2 d 2 = ( x − ( − 6 ) ) 2 + ( y − 0 ) 2 d 2 = ( x + 6 ) 2 + y 2 It is given that the sum of the distance from ( x , y ) to ( 6 , 0 ) and ( − 6 , 0 ) is 20

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

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 27E

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The equation of an ellipse with center at (0,0), whose sum of the distance from (x,y) to (6,0) and (−6,0) is 20.

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Chapter 21.5, Problem 26E

Chapter 21.5, Problem 28E

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Chapter 21 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

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 equation of an ellipse with center at ( 0 , 0 ) , whose sum of the distance from ( x , y ) to ( 6 , 0 ) and ( − 6 , 0 ) is 20.

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The equation of an ellipse with center at (0,0), whose sum of the distance from (x,y) to (6,0) and (−6,0) is 20.

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Chapter 21 Solutions