Locus of centre of circle in Lambert theorem

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A beautiful theorem, when three tangents to a parabola form a triangle,the focus of the parabola lies on the circumcircle of the triangle. But what is the locus of the centre of the circumcircle of the triangle? Using web or library resources I haven't been able to find a relevant link or page and the demonstration (which I don't ask for) is too challenging for me.