Inner Orthoptic of an ellipse

Inner Orthoptic curve of an ellipse

WLOG the ellipse is given with one parameter. Variations of the parameter k change the eccentricity. The orthoptic curve of the given ellipse is the geometric locus of points through which passes a pair of perpendicular tangents to the ellipse. It is called the director circle. The inner orthoptic of an ellipse is also an ellipse. It is easy to show that the gicen ellipse and its inner orthoptic have different foci and eccentricity.
This applet is a companion for a paper with Witold Mozgawa, which will appear in Journal of Geometry.