Explanation Given: The equation of the circle is, x 2 + y 2 + 10 x + 8 y + 5 = 0 Formula Used: The general equation of a circle of radius r with center ( h , k ) is ( x − h ) 2 + ( y − k ) 2 = r 2 Calculation: To find the center and radius of the circle x 2 + y 2 + 10 x + 8 y + 5 = 0 , complete the squares in x and y as below: First, add 16 to the both sides of the above equation. x 2 + y 2 + 10 x + 8 y + 5 + 16 = 16 x 2 + 10 x + ( y 2 + 8 y + 16 ) + 4 = 16 x 2 + 10 x + ( y + 4 ) 2 = 16 − 5 x 2 + 10 x + ( y + 4 ) 2 = 11 Now, add 4 to the both sides of the above equation

Mathematical Ideas (13th Edition) - Standalone book

13th Edition

ISBN: 9780321977076

Author: Charles D. Miller, Vern E. Heeren, John Hornsby, Christopher Heeren

Publisher: PEARSON

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Chapter 8.1, Problem 40E

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To calculate: The radius and center of the circle x2+y2+10x+8y+5=0

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Chapter 8.1, Problem 39E

Chapter 8.1, Problem 41E

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Chapter 8 Solutions

Mathematical Ideas (13th Edition) - Standalone book

Ch. 8.1 - Fill in each blank with the correct response. 1....Ch. 8.1 - Fill in each blank with the correct response. For...Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Locate the following points on the rectangular...Ch. 8.1 - Locate the following points on the rectangular...Ch. 8.1 - Prob. 9E Ch. 8.1 - Locate the following points on the rectangular...

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The radius and center of the circle x 2 + y 2 + 10 x + 8 y + 5 = 0

Solution Summary: The author calculates the radius and center of a circle by adding 16 to the two sides of the equation.

To calculate: The radius and center of the circle x2+y2+10x+8y+5=0

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Chapter 8 Solutions