Explanation Formula used: Ellipses with center at ( h , k ) and major axis parallel to a coordinate axis. Center Major Axis Foci Vertices Equation ( h , k ) Parallel to x -axis ( h + c , k ) , ( h − c , k ) ( h + a , k ) , ( h − a , k ) ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 a > b and b 2 = a 2 − c 2 ( h , k ) Parallel to y -axis ( h , k + c ) , ( h , k − c ) ( h , k + a ) , ( h , k − a ) ( x − h ) 2 b 2 + ( y − k ) 2 a 2 = 1 a > b and b 2 = a 2 − c 2 Calculation: It is known that the foci will always lie on the axis of symmetry. Also note that the focus and vertices lies on the same vertical line x = − 1 . This implies that the axis of symmetry is parallel to the y -axis. Thus, equation will be of the form ( x − h ) 2 b 2 + ( y − k ) 2 a 2 = 1 . It is known that center lies between the vertices. Thus, the center is, C = ( − 1 − 1 2 , 7 − 3 2 ) = ( − 2 2 , 4 2 ) = ( − 1 , 2 ) Therefore, the center is ( h , k ) = ( − 1 , 2 )

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

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 12, Problem 14T

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An equation of the ellipse whose vertices at (−1,7) and (−1,−3);focus at(−1,−1).

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An equation of the ellipse whose vertices at ( − 1 , 7 ) and ( − 1 , − 3 ) ;focus at ( − 1 , − 1 ) .

Solution Summary: The author explains the equation of the ellipse whose vertices at (x+1)216+

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An equation of the ellipse whose vertices at (−1,7) and (−1,−3);focus at(−1,−1).

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