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 − 1 ) 2 36 + ( y + 4 ) 2 100 = 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 − 1 ) 2 36 + ( y + 4 ) 2 100 = 1 with ( x − h ) 2 b 2 + ( y − k ) 2 a 2 = 1 and observe that the center is ( h , k ) = ( 1 , − 4 ) , a 2 = 100 and b 2 = 36 . This implies that a = 10 and b = 6 . Therefore, foci and vertices of the form ( h , k ± c ) and ( h , k ± a )

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 12.4, Problem 34E

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To graph: An ellipse whose equation is (x−1)236+(y+4)2100=1.

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Chapter 12.4, Problem 33E

Chapter 12.4, Problem 35E

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To graph: An ellipse whose equation is ( x − 1 ) 2 36 + ( y + 4 ) 2 100 = 1 .

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

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To graph: An ellipse whose equation is (x−1)236+(y+4)2100=1.

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Chapter 12 Solutions