The coefficients of a circle

  Find the coefficients a, b, c, d of the circle,
      
      ax**2 + ay**2 + bx + cy + d  = 0 
      
    which crosses these three points   
         
      (x[1],y[1])  (x[2],y[2])  (x[3],y[3])  
      
    Using the three points we obtain the matrix.
 
 (a)x**2   (a)y**2   (b)x      (c)y        (d) = 0               
    x[1]**2   y[1]**2   x[1]      y[1]      1    0
    x[2]**2   y[2]**2   x[2]      y[2]      1    0
    x[3]**2   y[3]**2   x[3]      y[3]      1    0
 
  This system has three lines and four unknowns (a, b, c, d).
  It is a homogeneous system, so it has an infinite number of solutions.
 
  To find a solution, I chose to set a = 1.
  We therefore have five rows and five unknowns. 
 
 (a)x**2   (a)y**2      x         y   
             
    1         0         0         0         0    1  
    0         1         0         0         0    1 
    x[1]**2   y[1]**2   x[1]      y[1]      1    0 
    x[2]**2   y[2]**2   x[2]      y[2]      1    0 
    x[3]**2   y[3]**2   x[3]      y[3]      1    0 
  
  All that remains is to solve the system.