Explanation Given: The equation of the ellipse is, 9 x 2 + 4 y 2 = 1 Approach: The following equation is the basic equation for an ellipse that is not centered at the origin. ( x − h ) 2 b 2 + ( y − k ) 2 a 2 = 1 With the following properties, Center C = ( h , k ) …… ( 1 ) Vertices V = ( 0 + h , ± a + k ) …… ( 2 ) Foci F = ( 0 + h , ± c + k ) …… ( 3 ) Where c 2 = a 2 − b 2 …… ( 4 ) Calculation: Consider the equation, 9 x 2 + 4 y 2 = 1 Convert the above equation into the standard equation of an ellipse. x 2 ( 1 9 ) + y 2 ( 1 4 ) = 1 ( x − 0 ) 2 ( 1 3 ) 2 + ( y − 0 ) 2 ( 1 2 ) 2 = 1 Compare the above equation of the ellipse with the standard equation of an ellipse. a = 1 2 b = 1 3 h = 0 k = 0 Calculate the center of the ellipse. Substitute 0 for h and 0 for k in the equation ( 1 ) . C = ( 0 , 0 ) Calculate the vertices of the ellipse. Substitute 1 2 for a , 0 for h and 0 for k in the equation ( 2 ) . V 1 = ( 0 + 0 , 1 2 + 0 ) = ( 0 , 1 2 ) Substitute − 1 2 for a , 0 for h and 0 for k in the equation ( 2 ) . V 2 = ( 0 + 0 , − 1 2 + 0 ) = ( 0 , − 1 2 ) Calculate the value of c To determine (b) The length of the major and minor axes. To determine (c) To sketch: The graph of the ellipse.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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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.CR, Problem 18E

To determine

(a)

To find:

The center, vertices, and foci of the ellipse.

To determine

(b)

The length of the major and minor axes.

To determine

(c)

To sketch:

The graph of the ellipse.

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Chapter 12.CR, Problem 17E

Chapter 12.CR, Problem 19E

Chapter 12 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 12.1 - A parabola is the set of all points in the plane...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 8E Ch. 12.1 - 5-10 Graphs of Parabolas Match the equation with...Ch. 12.1 - Prob. 10E

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(a) To find: The center, vertices, and foci of the ellipse.

Solution Summary: The author explains the basic equation for an ellipse that is not centered at the origin.

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(a) To find: The center, vertices, and foci of the ellipse.

(b) The length of the major and minor axes.

(c) To sketch: The graph of the ellipse.

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Chapter 12 Solutions

(a)

To find:

The center, vertices, and foci of the ellipse.

(b)

The length of the major and minor axes.

(c)

To sketch:

The graph of the ellipse.