Explanation Given information: Center at ( 1 , 2 ) , focus at ( 4 , 2 ) and contains the point ( 1 , 5 ) . Explanation: The center of the ellipse is at ( h , k ) = ( 1 , 2 ) , so h = 1 and k = 2 . The center and focus lie on the line y = 2 , hence the major axis is parallel to the x -axis. The distance from the center ( 1 , 2 ) to the focus ( 4 , 2 ) is c = 3 and the distance from the center ( 1 , 2 ) and the minor axis is b . The point given on the minor axis is ( 1 , 5 ) hence b = 3 . Thus, a 2 = b 2 + c 2 = 3 2 + 3 2 = 18 . The equation of ellipse is; ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 . Substitute h = 1 , k = 2 , a 2 = 18 and b 2 = 3 2 = 9 . Therefore, the equation of ellipse is ( x − 1 ) 2 18 + ( y − 2 ) 2 9 = 1

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

4th Edition

ISBN: 9780134686974

Author: Michael Sullivan, Michael Sullivan III

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 9.3, Problem 63AYU

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The equation of the ellipse with center at (1,2), focus at (4,2) and contains the point (1,5), and then graph the equation.

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Chapter 9.3, Problem 62AYU

Chapter 9.3, Problem 64AYU

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Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

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The equation of the ellipse with center at ( 1 , 2 ) , focus at ( 4 , 2 ) and contains the point ( 1 , 5 ) , and then graph the equation.

Solution Summary: The author explains the equation of the ellipse with center at (1,2), focus and the point on the minor axis.

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The equation of the ellipse with center at (1,2), focus at (4,2) and contains the point (1,5), and then graph the equation.

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Chapter 9 Solutions