Explanation Given information: Center at ( 2 , − 2 ) ; Vertex at ( 7 , − 2 ) ; Focus at ( 4 , − 2 ) . Explanation: The center of the ellipse is at ( h , k ) = ( 2 , − 2 ) , so h = 2 and k = − 2 . The center, focus and vertex all lie on the line y = − 2 , hence the major axis is parallel to the x-axis. The distance from the center ( 2 , − 2 ) to the focus ( 4 , − 2 ) is c = 2 and the distance from the center ( 2 , − 2 ) to the vertex ( 7 , − 2 ) is a = 5 . Thus, b 2 = a 2 − c 2 = 5 2 − 2 2 = 21 . The equation of ellipse is; ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 . Substitute h = 2 , k = − 2 , a 2 = 5 2 = 25 and b 2 = 21 , Therefore, the equation of ellipse is ( x − 2 ) 2 25 + ( y + 2 ) 2 21 = 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 55AYU

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The equation of the ellipse with center at (2,−2), vertex at (7,−2) and focus at (4,−2), and the graph the equation.

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Chapter 9.3, Problem 54AYU

Chapter 9.3, Problem 56AYU

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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 ( 2 , − 2 ) , vertex at ( 7 , − 2 ) and focus at ( 4 , − 2 ) , and the graph the equation.

Solution Summary: The author explains the equation of the ellipse with center at (x-2)225+

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The equation of the ellipse with center at (2,−2), vertex at (7,−2) and focus at (4,−2), and the graph the equation.

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