Question 1 The standard equation of a circle is: 1 x² + y² + Ax+By+ C = 0 Show that the following systems of linear equations must be satisfied when the circle passes through the points (-2; 4) (3; -1) and (6; 8): (Z) 2A-4BC = 20 3AB+C = -10 (6A + 8B + C = -100 Calculate B in system (Z) using Cramer's rule. How can the system of equations (Z) be represented graphically? How can the solution to the system of equations (Z) be represented graphically?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question 1
The standard equation of a circle is:
1
x² + y² + Ax+By+C =0
Show that the following systems of linear equations must be satisfied when the circle passes
through the points (-2; 4) (3; -1) and (6; 8):
2A-4BC = 20
(Z) 3AB+C = -10
(6A +8B + C = -100
Calculate B in system (Z) using Cramer's rule.
How can the system of equations (Z) be represented graphically?
How can the solution to the system of equations (Z) be represented graphically?
Transcribed Image Text:Question 1 The standard equation of a circle is: 1 x² + y² + Ax+By+C =0 Show that the following systems of linear equations must be satisfied when the circle passes through the points (-2; 4) (3; -1) and (6; 8): 2A-4BC = 20 (Z) 3AB+C = -10 (6A +8B + C = -100 Calculate B in system (Z) using Cramer's rule. How can the system of equations (Z) be represented graphically? How can the solution to the system of equations (Z) be represented graphically?
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