There are two ways the coefficient matrix for a conic section can have two (or more) free parameters:
I) Four or five points lie on the same line
II) Two or more points coincide.
Since the [i]algebraic system[/i] is not uniquely determined, ought we not be able to conclude that the conic section is not uniquely determined?
Well, [i]no.[/i] Vonsider the first case...
