
  Find the coefficients a, b, c, d, e, of the curve,
       
       ax**2 + by**2 + cx + dy + e  = 0 

        that passes through this four points.    
          
       (x[1],y[1])  (x[2],y[2])  (x[3],y[3])  (x[4],y[4]) 

  Using the given points, we obtain this matrix.

  (a)x**2   (b)y**2   (c)x      (d)y        (e) = 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
     x[4]**2   y[4]**2   x[4]      y[4]      1    0

  This system has four rows (4 points), and five value to find (a, b, c, d, e).
  If the system is consistent, it will have many solutions.

  To find one solution, I must give a value, to one of a coefficient.
  I have chosen to write e = 1/1.

  we obtain this matrix.
              
     x[1]**2   y[1]**2   x[1]      y[1]      1/1  0/1
     x[2]**2   y[2]**2   x[2]      y[2]      1/1  0/1
     x[3]**2   y[3]**2   x[3]      y[3]      1/1  0/1
     x[4]**2   y[4]**2   x[4]      y[4]      1/1  0/1
     0/1       0/1       0/1       0/1       1/1  1/1

  Now you can use gaussjordan() on the matrix,
  to find the value of a, b, c, d, e.
