Explanation Definition used: Standard equation of an ellipse with center at ( h , k ) : Major axis horizontal: ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 , a > b > 0 . The vertices are ( h − a , k ) , ( h + a , k ) , length of the minor axis is 2 b and foci are ( h − c , k ) , ( h + c , k ) , where c 2 = a 2 − b 2 . Major axis vertical: ( x − h ) 2 b 2 + ( y − k ) 2 a 2 = 1 , a > b > 0 . The vertices are ( h , k − a ) , ( h , k + a ) , length of the minor axis is 2 b and foci are ( h , k − c ) , ( h , k + c ) , where c 2 = a 2 − b 2 . Calculation: The given equation of the ellipse is 4 x 2 + 9 y 2 − 16 x + 18 y − 11 = 0 . Convert the equation of an ellipse 4 x 2 + 9 y 2 − 16 x + 18 y − 11 = 0 into standard form as follows. 4 x 2 + 9 y 2 − 16 x + 18 y − 11 = 0 4 ( x 2 − 4 x ) + 9 ( y 2 + 2 y ) = 11 4 ( x 2 − 4 x + 4 ) + 9 ( y 2 + 2 y + 1 ) = 11 + 16 + 9 4 ( x − 2 ) 2 + 9 ( y + 1 ) 2 = 36 Simplify further as follows. 4 ( x − 2 ) 2 36 + 9 ( y + 1 ) 2 36 = 1 [ Divide both the sides with 36 ] ( x − 2 ) 2 9 + ( y + 1 ) 2 4 = 1 ( x − 2 ) 2 3 2 + ( y − ( − 1 ) ) 2 2 2 = 1 Clearly, the equation ( x − 2 ) 2 3 2 + ( y − ( − 1 ) ) 2 2 2 = 1 is in the form of ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

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 43E

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The center, the vertices and the foci of the ellipse with the equation 4x2+9y2−16x+18y−11=0 and sketch the graph of the ellipse.

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Chapter 7.2, Problem 42E

Chapter 7.2, Problem 44E

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Chapter 7 Solutions

College Algebra: Graphs and Models (6th Edition)

Ch. 7.1 - In Exercises 16, match the equation with one of...Ch. 7.1 - Prob. 2E Ch. 7.1 - In Exercises 16, match the equation with one of...Ch. 7.1 - In Exercises 16, match the equation with one of...Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Find the vertex, the focus, and the directrix....Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Find the vertex, the focus, and the directrix....

Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Prob. 19E Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Prob. 21E Ch. 7.1 - Find an equation of a parabola satisfying the...Ch. 7.1 - Find the vertex, the focus, and the directrix....Ch. 7.1 - Find the vertex, the focus, and the directrix....Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Find the vertex, the focus, and the directrix....Ch. 7.1 - Prob. 29E Ch. 7.1 - Find the vertex, the focus, and the directrix....Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Flashlight Mirror. A heavy-duty flashlight mirror...Ch. 7.1 - Ultrasound Receiver. Information Unlimited...Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Consider the following linear equations. Without...Ch. 7.1 - Consider the following linear equations. Without...Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Consider the following linear equations. Without...Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Suspension Bridge. 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Then find the...Ch. 7 - Prob. 38RE Ch. 7 - Prob. 39RE Ch. 7 - Prob. 40RE Ch. 7 - Prob. 41RE Ch. 7 - Prob. 42RE Ch. 7 - Prob. 43RE Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Navigation. Two radio transmitters positioned 400...Ch. 7 - Prob. 1T Ch. 7 - Prob. 2T Ch. 7 - Prob. 3T Ch. 7 - Prob. 4T Ch. 7 - Prob. 5T Ch. 7 - Prob. 6T Ch. 7 - Prob. 7T Ch. 7 - Prob. 8T Ch. 7 - Prob. 9T 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 Ch. 7 - Prob. 17T Ch. 7 - Prob. 18T Ch. 7 - Prob. 19T Ch. 7 - Prob. 20T Ch. 7 - Graph the system of inequalities. Then find the...Ch. 7 - Prob. 22T Ch. 7 - Prob. 23T

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The center, the vertices and the foci of the ellipse with the equation 4 x 2 + 9 y 2 − 16 x + 18 y − 11 = 0 and sketch the graph of the ellipse.

Solution Summary: The author sketched the ellipse's center, vertices, and foci with the equation 4x2+9y 2-16x+18y-11=0

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The center, the vertices and the foci of the ellipse with the equation 4x2+9y2−16x+18y−11=0 and sketch the graph of the ellipse.

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Chapter 7 Solutions