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I don't know the reason, but you are right and it is very funny, for example sqrt(17) gives a closed circle, sqrt(19) does not.

Using a numerical approximation seems to create closed circles in any case.

a = sqrt(2).n()
plot(sqrt(a^2-x^2),-a,a,aspect_ratio=1)+plot(-sqrt(a^2-x^2),-a,a)