Explanation Formula used: The Distance formula: The distance between two points P 1 = ( x 1 , y 1 ) and P 2 = ( x 2 , y 2 ) , denoted by d ( P 1 , P 2 ) is d ( P 1 , P 2 ) = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 . The Midpoint formula: The midpoint M = ( x , y ) of the line segments from P 1 = ( x 1 , y 1 ) to P 2 = ( x 2 , y 2 ) , is M = ( x 1 + x 2 2 , y 1 + y 2 2 ) . Definition used: The graph of any equation of the form ( x − h ) 2 + ( y − k ) 2 = r 2 is a circle with radius r and center ( h , k ) . Calculation: From the given figure observe that the center is the midpoint of ( 2 , 3 ) and ( 8 , 3 ) . Substitute ( x 1 , y 1 ) = ( 2 , 3 ) and ( x 2 , y 2 ) = ( 8 , 3 ) in the midpoint formula. ( h , k ) = ( x 1 + x 2 2 , y 1 + y 2 2 ) = ( 2 + 8 2 , 3 + 3 2 ) = ( 10 2 , 6 2 ) = ( 5 , 3 ) Therefore, the center is ( h , k ) = ( 5 , 3 )

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

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Chapter 12, Problem 14RE

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The center and radius of the given circle and express it in standard form.

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Chapter 12 Solutions

Elementary & Intermediate Algebra

Ch. 12.1 - The distance between two points P1 =...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - In Problems 3 and 4, find the distance between the...Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E

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The center and radius of the given circle and express it in standard form.

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The center and radius of the given circle and express it in standard form.

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Chapter 12 Solutions