To determine The center and foci of the ellipse 2 x 2 + 3 y 2 − 8 x + 18 y + 29 = 0 . Explanation Definition used: The ellipse with center ( h , k ) and whose major axis parallel to x axis is ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 . The ellipse with center ( h , k ) and whose major axis parallel to y axis is ( y − k ) 2 a 2 + ( x − h ) 2 b 2 = 1 . Calculation: Rewrite 2 x 2 + 3 y 2 − 8 x + 18 y + 29 = 0 as, 2 x 2 − 8 x + 3 y 2 + 18 y + 29 = 0 2 ( x 2 − 4 x ) + 3 ( y 2 + 6 y ) = − 29 2 ( x 2 − 4 x + 4 ) + 3 ( y 2 + 6 y + 9 ) = 6 2 ( x − 2 ) 2 + 3 ( y + 3 ) 2 = 6 Simplify further as, 2 ( x − 2 ) 2 6 + 3 ( y + 3 ) 2 6 = 6 6 ( x − 2 ) 2 3 + ( y + 3 ) 2 2 = 1

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

11th Edition

ISBN: 9780137554843

Author: Allyn 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 21.7, Problem 1PE

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The center and foci of the ellipse 2x2+3y2−8x+18y+29=0.

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Chapter 21.6, Problem 54E

Chapter 21.7, Problem 1E

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Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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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