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 ) and ( h − c , k ) ( h + a , k ) and ( 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 ) and ( h , k − c ) ( h , k + a ) and ( h , k − a ) ( x − h ) 2 b 2 + ( y − k ) 2 a 2 = 1 a > b and b 2 = a 2 − c 2 Calculation: The equation of the ellipse is ( x − 3 ) 2 9 + ( y + 2 ) 2 25 = 1 . Note that the denominator of the y 2 term has the largest number. Thus the given ellipse has y -axis as the major axis. Compare the equation ( x − 3 ) 2 9 + ( y + 2 ) 2 25 = 1 with ( x − h ) 2 b 2 + ( y − k ) 2 a 2 = 1 and observe that the center is ( h , k ) = ( 3 , − 2 ) , a 2 = 25 and b 2 = 9 . This implies that a = 5 and b = 3

4th Edition

ISBN: 9780134556079

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

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 12.4, Problem 33E

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To graph: An ellipse whose equation is (x−3)29+(y+2)225=1.

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Chapter 12.4, Problem 32E

Chapter 12.4, Problem 34E

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To graph: An ellipse whose equation is ( x − 3 ) 2 9 + ( y + 2 ) 2 25 = 1 .

Solution Summary: The author calculates an ellipse with a center at (h,k) and major axes parallel to the coordinate axis.

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To graph: An ellipse whose equation is (x−3)29+(y+2)225=1.

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