Explanation Given: The equation of the ellipse is, x 2 + 4 y 2 = 16 Approach: The following equation is the basic equation for an ellipse that is not centered at the origin. ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1 With the following properties, Center C = ( h , k ) …… ( 1 ) Vertices V = ( ± a + h , 0 + k ) …… ( 2 ) Foci F = ( ± c + h , 0 + k ) …… ( 3 ) Where c 2 = a 2 − b 2 …… ( 4 ) Calculation: Consider the equation, x 2 + 4 y 2 = 16 Convert the above equation into the standard equation of an ellipse. x 2 16 + 4 y 2 16 = 1 x 2 16 + y 2 4 = 1 ( x − 0 ) 2 4 2 + ( y − 0 ) 2 2 2 = 1 Compare the above equation of the ellipse with the standard equation of an ellipse. a = 4 b = 2 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 4 for a , 0 for h and 0 for k in the equation ( 2 ) . V 1 = ( 4 + 0 , 0 + 0 ) = ( 4 , 0 ) Substitute − 4 for a , 0 for h and 0 for k in the equation ( 2 ) To determine (b) The length of the major and minor axes. To determine (c) To sketch: The graph of the ellipse.

4th Edition

ISBN: 8220100548512

Author: Watson

Publisher: CENGAGE L

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Chapter 12.CR, Problem 17E

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 16E

Chapter 12.CR, Problem 18E

Chapter 12 Solutions

EBK ALGEBRA AND TRIGONOMETRY

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 that the following equation is 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.