How to draw lines 'tangent' to ellipses?

What is the best and most accurate way of drawing a line between the edge of these two ellipses? When drawing a line between two circles, we use osnap to tangent but this doesn't seem to work. Any ideas would be much appreciated.

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Well, It's an "old school" way.... Long way around.... But you can draw a line from the same Quadrant on one ellipse to the same quadrant on the second ellipse.
Then draw a line out in space that is perpendicular to the line you just created.
Then move your first line (Quad to Quad) to the intersections of the ellipse and the perpendicular lines...
But other than that, you would have to regenerate the ellipse with the polyline command and arcs or arc commands and is much more time consuming.

 
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