Explanation Result used: The given equation is symmetric to the x -axis if no change in the equation when replace y by − y . The given equation is symmetric to the y -axis if no change in the equation when replace x by − x . The given equation is symmetric to the origin if no change in the equation when replace x by − x and y by − y . Calculation: Consider the given equation 3 x 2 + 3 y 2 + 6 y − 20 = 0 . The graph of the given circle equation in figure1 as follows. In order to find the given equation 3 x 2 + 3 y 2 + 6 y − 20 = 0 is symmetric to the x -axis replace y by − y as follows, 3 x 2 + 3 y 2 + 6 y − 20 = 0 3 x 2 + 3 ( − y ) 2 + 6 ( − y ) − 20 = 0 3 x 2 + 3 y 2 − 6 y − 20 = 0 The replacement of y by − y does change the given equation 3 x 2 + 3 y 2 + 6 y − 20 = 0 . Therefore, the given equation 3 x 2 + 3 y 2 + 6 y − 20 = 0 is not symmetric to the x -axis

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 21.3, Problem 3PE

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Whether the circle 3x2+3y2+6y−20=0 is symmetric to the x-axis, y-axis, origin.

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Chapter 21.3, Problem 2PE

Chapter 21.3, Problem 1E

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Chapter 21 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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Whether the circle 3 x 2 + 3 y 2 + 6 y − 20 = 0 is symmetric to the x -axis, y -axis, origin.

Whether the circle 3x2+3y2+6y−20=0 is symmetric to the x-axis, y-axis, origin.

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Chapter 21 Solutions