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 5 x 2 + 5 y 2 − 10 x + 20 y = 3 . Sketch the graph of the circle equation 5 x 2 + 5 y 2 − 10 x + 20 y = 3 in figure1 as follows, In order to find the given equation 5 x 2 + 5 y 2 − 10 x + 20 y = 3 is symmetric to the x -axis replace y by − y as follows, 5 x 2 + 5 y 2 − 10 x + 20 y = 3 5 x 2 + 5 ( − y ) 2 − 10 x + 20 ( − y ) = 3 5 x 2 + 5 y 2 − 10 x − 20 y = 3 The replacement of y by − y does change the given equation 5 x 2 + 5 y 2 − 10 x + 20 y = 3 . Therefore, the given equation 5 x 2 + 5 y 2 − 10 x + 20 y = 3 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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Question

Chapter 21.3, Problem 40E

To determine

Whether: The circle 5x2+5y2−10x+20y=3 is symmetric to either axis or the origin.

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Chapter 21.3, Problem 39E

Chapter 21.3, Problem 41E

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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 5 x 2 + 5 y 2 − 10 x + 20 y = 3 is symmetric to either axis or the origin.

Whether: The circle 5x2+5y2−10x+20y=3 is symmetric to either axis or the origin.

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Chapter 21 Solutions