Explanation Given Information: The equation of a circle, x 2 + y 2 + 4 x + 4 y − 1 = 0 Formula used: Standard form of the circle ( x − h ) 2 + ( y − k ) 2 = r 2 . Calculation: In order to find the radius and center of a circle, group the x terms together and then y terms together. x 2 + y 2 + 4 x + 4 y − 1 = 0 x 2 + 4 x + y 2 + 4 y − 1 = 0 Now take the coefficient of x- term multiply it by 1 2 and square it, and then add this on both sides of the equation. Do the same with the y -term coefficient. Here coefficient of x is 4 and coefficient of y is 4. So multiply them by 1 2 and then square them both. Half of 4 is 2 and the square of 2 is 4. Add 4 on both sides of the equation as shown and do the same with the y -term coefficient. x 2 + 4 x + 4 + y 2 + 4 y + 4 = 1 + 4 + 4 ( x 2 + 4 x + 4 )

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Chapter 13.3, Problem 4PE

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To calculate: The center and radius of a circle whose equation is x2+y2+4x+4y−1=0.

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Chapter 13 Solutions

Beginning and Intermediate Algebra

Ch. 13.1 - Find the distance between the points ( − 4 , − 2 )...Ch. 13.1 - Prob. 2SP Ch. 13.1 - Prob. 3SP Ch. 13.1 - Prob. 4SP Ch. 13.1 - Prob. 5SP Ch. 13.1 - Prob. 6SP Ch. 13.1 - Prob. 7SP Ch. 13.1 - Prob. 8SP Ch. 13.1 - Prob. 1PE Ch. 13.1 - Prob. 2PE

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The center and radius of a circle whose equation is x 2 + y 2 + 4 x + 4 y − 1 = 0 .

Solution Summary: The author explains how to calculate the center and radius of a circle.

To calculate: The center and radius of a circle whose equation is x2+y2+4x+4y−1=0.

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Chapter 13 Solutions