There is an ellipse \(d\) with semi-major axis \(a\) and semi-minor axis \(b\). There is another ellipse \(e\) inscribed inside ellipse \(d\) with two points tangent.

For all the triangles \(T_i\) for which \(d\) is Steiner inellipse, \(e\) is locus of their circumcenters.

Find \(\left(\dfrac{a}{b} \right)^2\).

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