Explanation Given information: Foci at ( 5 , 1 ) and ( − 1 , 1 ) , and length of major axis is 8 . Explanation: The ellipse has Foci at ( 5 , 1 ) and ( − 1 , 1 ) both lie on the line y = 1 , hence the major axis is parallel to the x -axis. The center of the ellipse is at midpoint of foci ( 5 , 1 ) and ( − 1 , 1 ) . Therefore, the center of the ellipse is ( 5 − 1 2 , 1 + 1 2 ) = ( 2 , 1 ) . The center of the ellipse is at ( h , k ) = ( 2 , 1 ) , so h = 2 and k = 1 . The distance from the center ( 2 , 1 ) to the focus ( 5 , 1 ) is c = 3 and length of major axis is 8 hence the distance between center and vertex, a = 8 2 = 4 . Thus, b 2 = a 2 − c 2 = 4 2 − 3 2 = 7 . The equation of ellipse is; ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1

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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 59AYU

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The equation of the ellipse with foci at (5,1) and (−1,1), and length of major axis is 8, and graph the equation.

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Chapter 9.3, Problem 58AYU

Chapter 9.3, Problem 60AYU

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Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)

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The equation of the ellipse with foci at ( 5 , 1 ) and ( − 1 , 1 ) , and length of major axis is 8 , and graph the equation.

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The equation of the ellipse with foci at (5,1) and (−1,1), and length of major axis is 8, and graph the equation.

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