A question on algebraic circle fitting

Given a finite number of points in the plane,
(x1,y1), (x2,y2), ..., (xn,yn),
the "algebraic way" to fit a circle to these points
is to minimize the sum

sum( (xi^2 + yi^2 + 2 D xi + 2 E yi + F)^2 , i = 1..n )

over the variables D,E,F.


Is it correct that the resulting minimizers
will satisfy the condition

D^2 + E^2 >= F ?


Under what conditions will minimizers D,E,F exist? -
A necessary condition is that not all points (xi,yi) lie on
a common line in case n >= 3. Is this condition also sufficient,
or what other conditions are there?
.

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