System of linear equations

  • #1
IniquiTrance
190
0

Homework Statement



Find coefficients a, b, c, d so that the circle with the following 3 points satisfies the equation:

[tex]ax^{2} + ay^{2} + bx + cy + d = 0[/tex]

Points:

(-4, 5)
(4, -3)
(-2, 7)



Homework Equations





The Attempt at a Solution


I'm wondering if since I can only construct 3 equations from the 3 points, if I will have to make one unknown a parameter - probably d.

Is there a way to construct a 4 th equation which I'm missing?

Thanks!
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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The parameters a,b,c and d are not independent if you are given that it's a circle. Write the equation of a circle in the form (x-a)^2+(y-b)^2=r^2. Now you only have three parameters. And you have three points.
 
Last edited:
  • #3
IniquiTrance
190
0
What if I used Gauss Jordan elimination to find a,b and c in terms of parameter d, would that sufficiently answer the question?
 
  • #4
Dick
Science Advisor
Homework Helper
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620
Sure, I suppose. The 'fourth parameter' is really that you can divide your whole equation by any one of the four parameters that is nonzero and eliminate it. It was never really there to begin with. I.e. x^2+y^2+bx+cy+d=0 is also just as good.
 
Last edited:

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