Explanation Calculation: Consider the given equation. x 2 + y 2 + A x + B y + C = 0 â€¦â€¦ (1) Substitute the first given point x , y = 2 , 2 in the given equation. x 2 + y 2 + A x + B y + C = 0 . 2 2 + 2 2 + A 2 + B 2 + C = 0 4 + 4 + 2 A + 2 B + C = 0 8 + 2 A + 2 B + C = 0 2 A + 2 B + C + 8 = 0 Consider the above equation as, 2 A + 2 B + C + 8 = 0 â€¦â€¦ (2) Substitute the second given point x , y = 6 , 0 in the equation x 2 + y 2 + A x + B y + C = 0 . 6 2 + 0 2 + A 6 + B 0 + C = 0 36 + 0 + 6 A + 0 + C = 0 6 A + C + 36 = 0 Consider the above equation as, 6 A + C + 36 = 0 â€¦â€¦ (3) Substitute the third given point x , y = 7 , 23 in the equation x 2 + y 2 + A x + B y + C = 0 . 7 2 + 23 2 + A 7 + B 23 + C = 0 49 + 529 + 7 A + 23 B + C = 0 578 + 7 A + 23 B + C = 0 7 A + 23 B + C + 578 = 0 Consider the above equation as, 7 A + 23 B + C + 578 = 0 â€¦â€¦ (4) Multiply equation (2) by 23 and rewrite as, 23 2 A + 2 B + C + 8 = 23 ⋅ 0 46 A + 46 B + 23 C + 184 = 0 Consider the above equation as, 46 A + 46 B + 23 C + 184 = 0 â€¦â€¦ (5) Multiply equation (4) by − 2 and rewrite as, − 2 7 A + 23 B + C + 578 = − 2 ⋅ 0 − 14 A − 46 B − 2 C − 1156 = 0 Consider the above equation as, − 14 A − 46 B − 2 C − 1156 = 0 â€¦â€¦ (6) Add equation (5) and equation (6) to eliminate B To determine To calculate: The center and radius of the circle for the given points 2 , 2 , 6 , 0 , 7 , 23 .

17th Edition

ISBN: 9780078035609

Author: Miller, Julie, Gerken, Donna.

Publisher: Mcgraw-hill Education,

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Question

Chapter 8.2, Problem 65PE

To determine

To calculate: An equation of the form x2+y2+Ax+By+C=0 that represents the circle that passes through the given points 2,2,6,0, and 7,23 .

To determine

To calculate: The center and radius of the circle for the given points 2,2,6,0,7,23 .

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Chapter 8.2, Problem 64PE

Chapter 8.2, Problem 66PE

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