Coxeter- Theorem 9.14 - Figure 9.1D
Theorem 9.14: Let Z be a variable point on the diagonal CE of a given pentagon ABCDE. Then the two points X=ZB·DE, Y=ZA·CD, determine a line XY whose envelope is the inscribed conic.
Construction of figure 9.1D: Pick five random points first, then construct a pentagon ABCDE. Connect CE, and pick a random point Z on CE. Then the two points X=ZB·DE, Y=ZA·CD. Then drag Z along CE, you will see the envelope formed by the line XY is a inscribed conic.