Explanation The standard form of the equation of an ellipse with its center at ( h , k ) is given by, ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 , where a , b > 0 The vertices of the ellipse are given by, ( h ± a , k ) and ( h , k ± b ) . Now, Consider the equation, ( x + 5 ) 2 4 + ( y + 3 ) 2 25 = 1 , which can be written in its standard form as follows, ( x + 5 ) 2 4 + ( y + 3 ) 2 25 = 1 ( x − ( − 5 ) ) 2 2 2 + ( y − ( − 3 ) ) 2 5 2 = 1 Compare the above equation with the standard form and it is observed that the center of the ellipse is ( − 5 , − 3 ) and a = 2 , b = 5

Pearson eText for Intermediate Algebra -- Instant Access (Pearson+)

8th Edition

ISBN: 9780137553464

Author: John Tobey, Jeffrey Slater

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, Problem 14RP

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The vertices and the center of the ellipse given by the equation (x+5)24+(y+3)225=1.

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Chapter 9, Problem 13RP

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Pearson eText for Intermediate Algebra -- Instant Access (Pearson+)

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The vertices and the center of the ellipse given by the equation ( x + 5 ) 2 4 + ( y + 3 ) 2 25 = 1 .

Solution Summary: The author explains the standard form of the equation of an ellipse with its center at (h,k).

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The vertices and the center of the ellipse given by the equation (x+5)24+(y+3)225=1.

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Chapter 9 Solutions