The Ellipse Inversion..

If $\frac{x^2}{16}$ + $\frac{y^2}{4}$ =1 is $\boxed{ellipse 1}$

Another ellipse, $\boxed{ellipse 2}$ with its minor axis being the major axis of ellipse 1 is drawn.

The foci of ellipse 2 and ends of minor axis of ellipse 1 coincide.

A tangent is drawn at one end of minor axis of ellipse 1 and an other parallel tangent is drawn at one end of major axis of ellipse 2 .

The sum of radii of circles that can be drawn touching both the tangents