The word "inellipse" is used in place of "ellipse inscribed".
In the worsheet we simply compute the drawing of a quadrilateral inellipse.
Some of the key points in Horvitz's paper :
using Marden's theorem
center of quadrilateral inellipse is lying in the segment linking midpoints of diagonals
2003 - Horvitz - The locus of centers of ellipses inscribed in quadrilaterals
Worlfram - Area inellipse given areal coordinates of center - http://mathworld.wolfram.com/Inellipse.html
Wolfram - Areal coordinates of point with respect to triangle - http://mathworld.wolfram.com/ArealCoordinates.html