The suggestion by @phcreates to use Scale1D is brilliant.
The direction of the 1D scaling determines the orientation of the ellipse, and the amount of scaling determines the eccentricity.
Draw a line parallel to the desired orientation of the ellipse.
Place three points on the line with the ratio the distance between point 1 and point 2 to the distance between point 1 and point 3 equal to the desired eccentricity.
Scale1D the lines with Copy=Yes. 1 is base, 3 is first reference point, 2 is second reference point.
Circle with Tangent option. The scaled lines are the tangent lines.
Scale1D the circle. 1 is the base, 2 is the first reference point, 3 is the second reference point.
