Explanation Formula used: The standard equation of the circle with center at ( h , k ) and radius r is ( x − h ) 2 + ( y − k ) 2 = r 2 . Calculation: The given points are ( 3 , − 2 ) , ( − 1 , − 4 ) and ( 2 , − 5 ) . The equation of a circle passes through ( 3 , − 2 ) is given by ( 3 − h ) 2 + ( − 2 − k ) 2 = r 2 . 9 + h 2 − 6 h + 4 + k 2 + 4 k = r 2 h 2 − 6 h + k 2 + 4 k + 13 = r 2 ...... ( 1 ) The equation of a circle passes through ( 2 , − 5 ) is given by ( 2 − h ) 2 + ( − 5 − k ) 2 = r 2 . 4 + h 2 − 4 h + 25 + k 2 + 10 k = r 2 h 2 − 4 h + k 2 + 10 k + 29 = r 2 ...... ( 2 ) The equation of a circle passes through ( − 1 , − 4 ) is given by ( − 1 − h ) 2 + ( − 4 − k ) 2 = r 2 . 1 + h 2 + 2 h + 16 + k 2 + 8 k = r 2 h 2 + 2 h + k 2 + 8 k + 17 = r 2 ...... ( 3 ) From the equations (1) and (2), h 2 − 6 h + k 2 + 4 k + 13 = h 2 − 4 h + k 2 + 10 k + 29 − 6 h + 4 k + 13 = − 4 h + 10 k + 29 2 h + 6 k + 16 = 0 2 h + 6 k = − 16

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 21, Problem 82RE

To determine

The equation of the circle that passes through the points (3,−2),(−1,−4) and (2,−5) by using the law of cosines.

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Chapter 21, Problem 81RE

Chapter 21, Problem 83RE

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Chapter 21 Solutions

Basic Technical Mathematics

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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The equation of the circle that passes through the points ( 3 , − 2 ) , ( − 1 , − 4 ) and ( 2 , − 5 ) by using the law of cosines.

The equation of the circle that passes through the points (3,−2),(−1,−4) and (2,−5) by using the law of cosines.

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Chapter 21 Solutions