Explanation Given that, the circle a x 2 + a y 2 + b x + c y + d = 0 passes through the points ( − 2 , 7 ) , ( − 4 , 5 ) , and ( 4 , − 3 ) . Since the points ( − 2 , 7 ) , ( − 4 , 5 ) , and ( 4 , − 3 ) passes through the circle a x 2 + a y 2 + b x + c y + d = 0 , they satisfy the circle equation a x 2 + a y 2 + b x + c y + d = 0 That is, a ( − 2 ) 2 + a ( 7 ) 2 + b ( − 2 ) + c ( 7 ) + d = 0 a ( − 4 ) 2 + a ( 5 ) 2 + b ( − 4 ) + c ( 5 ) + d = 0 a ( 4 ) 2 + a ( − 3 ) 2 + b ( 4 ) + c ( − 3 ) + d = 0 Simplify and rewrite the above system of equations as follows. d − 2 b + 7 c + 53 a = 0 d − 4 b + 5 c + 41 a = 0 d + 4 b − 3 c + 25 a = 0 The augmented matrix of the above-simplified system is, [ 1 − 2 7 53 0 1 − 4 5 41 0 1 4 − 3 25 0 ] Add − 1 times the first row to second and third row as shown below. [ 1 − 2 7 53 0 0 2 2 12 0 0 − 6 10 28 0 ] Multiply the second row by 1 2 as shown below. [ 1 − 2 7 53 0 0 1 1 6 0 0 − 6 10 28 0 ] Add 6 times the second row to third row as follows

12th Edition

ISBN: 9781119762911

Author: Anton

Publisher: WILEY

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Chapter 1.2, Problem 38E

To determine

The values of a, b, c and d for which the circle ax2+ay2+bx+cy+d=0 passes through the points (−2,7),(−4,5), and (4,−3).

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Chapter 1.2, Problem 37E

Chapter 1.2, Problem 39E

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Chapter 1 Solutions

ELEMENTARY LINEAR ALGEBRA-W/ACCESS

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The values of a , b , c and d for which the circle a x 2 + a y 2 + b x + c y + d = 0 passes through the points ( − 2 , 7 ) , ( − 4 , 5 ) , and ( 4 , − 3 ) .

The values of a, b, c and d for which the circle ax2+ay2+bx+cy+d=0 passes through the points (−2,7),(−4,5), and (4,−3).

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