Can we find the circles through the points where two ellipses meet?

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Show that the equation of any circle passing through the points of intersection of the ellipse \[(x + 2)^2 + 2y^2 = 18\] and the ellipse \[9(x - 1)^2 + 16y^2 = 25\] can be written in the form \[x^2 - 2ax + y^2 = 5 - 4a.\]