Look on the perimeter of the ellipse. Search for a line that sits on the exterior of the shape's perimeter. The tangent of an ellipse does not dissect the shape nor is it at a distance where it is not in contact with the shape.
Observe the contact point between the ellipse and the tangent. The tangent of an ellipse can only come into contact with the shape at a single point. If there is somehow more than one point of contact, this is not an ellipse tangent.
The angles between the tangent lines and the generator lines must always be equal to one another. The generator lines are the two lines within the confines of the ellipse perimeter that run from focus points to any point on the interior of the perimeter. Focus points are two places in the ellipse that lie on the longest axis and are spread equidistant from the center of the ellipse