Explanation Given information: Vertices at ( 2 , 5 ) and ( 2 , − 1 ) ; c = 2 . Explanation: The ellipse has vertices at ( 2 , 5 ) and ( 2 , − 1 ) both lie on the line x = 2 , hence the major axis is parallel to the y -axis. The center of the ellipse is at midpoint of vertices ( 2 , 5 ) and ( 2 , − 1 ) . Therefore, the center of the ellipse is ( 2 + 2 2 , 5 − 1 2 ) = ( 2 , 2 ) . The center of the ellipse is at ( h , k ) = ( 2 , 2 ) , so h = 2 and k = 2 . The distance from the center ( 2 , 2 ) to the focus is c = 2 and the distance from the center ( 2 , 2 ) to the vertex ( 2 , 5 ) is a = 3 . Thus, b 2 = a 2 − c 2 = 3 2 − 2 2 = 5 . The equation of ellipse is; ( x − h ) 2 b 2 + ( y − k ) 2 a 2 = 1

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Author: Sullivan

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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 9.3, Problem 60AYU

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The equation of the ellipse with vertices at (2,5) and (2,−1); c=2 and graph the equation.

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Chapter 9.3, Problem 59AYU

Chapter 9.3, Problem 61AYU

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