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.