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 \[x^2 - 2ax + y^2 = 5 - 4a.\]

Can we sketch the ellipses roughly? In how many points will the two ellipses meet? How can we find these points?

Where will the centres of circles going through the intersection points lie?

The two ellipses appear here in red. A possible circle through their intersections is in blue.