Tangency to two ellipses how?

I have arbitrary ellipse with center at <x,y>, major and minor axis <a,b> parallel to x and y axis, respectively, and a point on it P <c+x,d+y> at arbitrary angle T where c=a*cos(T) and d=b*sin(T).  If the major axis is a, the angle of tangency is atan2(d,a/cos(T)-c), and if the major axis is b, the angle is atan2(b/cos(90-T)-d,c).

The standard form of the tangent is y=tan(T)*x+(d+y)-tan(T)*(c+x).

I have two ellipses with arbitrary loci and axes.  How do I with similar simplicity determine the four lines of tangency those ellipses share?

>>3
I'd to see a picture of that.  Can you post some