Explanation Given: The coordinates of foci are ( − 3 , − 3 ) , ( 7 , − 3 ) and a point on ellipse is ( 2 , 1 ) Concept: The equation of the ellipse with the center at ( h , k ) , vertices at ( h ± a , k ) and foci at ( h ± c , k ) is written as ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 , where a > b > 0 and c 2 = a 2 − b 2 . Major axis of this ellipse is vertical. Calculation: It is given that the foci of ellipse are ( − 3 , − 3 ) and ( 7 , − 3 ) .and the point on ellipse is ( 2 , 1 ) . It is given that foci are ( − 3 , − 3 ) and ( 7 , − 3 ) . Compare the given foci with the coordinates of foci ( h ± c , k ) of the standard form of ellipse. h − c = − 3 ...... ( 1 ) h + c = 7 ...... ( 2 ) To calculate the value of h , add equation (1) and (2). h + c = 7 h − c = − 3 _ 2 h = 4 Further solve the above equation. 2 h = 4 h = 4 2 h = 2 Substitute the value of h in equation (1) to calculate the value of c . 2 − c = − 3 c = 2 + 3 c = 5 Substitute the coordinates of center ( h , k ) ≡ ( 2 , − 3 ) in the standard form of ellipse ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 . ( x − 2 ) 2 a 2 + ( y − ( − 3 ) ) 2 b 2 = 1 ( x − 2 ) 2 a 2 + ( y + 3 ) 2 b 2 = 1 A point on ellipse is ( 2 , 1 )

A Graphical Approach To College Algebra Custom Edition For Moraine Valley Community College

7th Edition

ISBN: 9780536452085

Author: HORNSBY, Lial, Rockswold

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 8.2, Problem 38E

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The equation of the ellipse with foci (−3,−3) and (7,−3) and a point on ellipse as (2,1).

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Chapter 8.2, Problem 37E

Chapter 8.2, Problem 39E

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Chapter 8 Solutions

A Graphical Approach To College Algebra Custom Edition For Moraine Valley Community College

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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Orbit of the Comet Swift-Tuttle Comet Swift–Tuttle...Ch. 8 - Prob. 61RE Ch. 8 - Prob. 62RE Ch. 8 - Prob. 63RE Ch. 8 - Prob. 64RE Ch. 8 - Prob. 1T Ch. 8 - Prob. 2T Ch. 8 - Prob. 3T Ch. 8 - Prob. 4T Ch. 8 - Prob. 5T Ch. 8 - Prob. 6T Ch. 8 - Prob. 7T Ch. 8 - Prob. 8T Ch. 8 - Graph each relation by hand. Identify the graph,...Ch. 8 - Prob. 10T Ch. 8 - Prob. 11T Ch. 8 - Prob. 12T Ch. 8 - Prob. 13T Ch. 8 - Prob. 14T Ch. 8 - Prob. 15T Ch. 8 - Prob. 16T

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The equation of the ellipse with foci ( − 3 , − 3 ) and ( 7 , − 3 ) and a point on ellipse as ( 2 , 1 ) .

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The equation of the ellipse with foci (−3,−3) and (7,−3) and a point on ellipse as (2,1).

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Chapter 8 Solutions