@dharr Your reply produces the full pencil of conics within and bordering the quadrilateral. I am deeply grateful for your insights into this problem's logic and Maple coding techniques.

@vv Your reply reveals a new approach of mapping a simple shape to a more complex one. Thank you for this food for thought.

@dharr Unfortunately your tips do not stop solve from running endlessly. I hope you will be able to return to this question with more time available.

In the meantime I am working on implementing in Maple the GeoGebra picture of an ellipse in a quadrilateral at https://www.geogebra.org/m/d4k6SjFX

@dharr Your reply is wonderful and gives me a base for attempting to display the other pencils in the book

@dharr Thanks for your correction.

What I really want is Maple code which produces a display that duplicates figure 3.20 in my worksheet. My own effort is quite wide of the mark.

The book referred to in my worksheet contains several more intriguing pencil figures. I would also like to reproduce these if someone can show me a general technique for doing so.

@acer Although Rouben Rostamian has shown that there is no need to refer to plot3d's output, it was interesting to work with MESH.

@Rouben Rostamian  Your method is both simpler and more beautiful!

@ Thank you.

@nm I appreciate your help

@Carl Love Good advice. I will follow it.

@acer Thank you for this. I will avoid using concatenated names from now on.

@acer I was not aware of the power of rationalize, so thank you for showing this to me.

@Rouben Rostamian  The solution to Harvard problem 15 is interesting. I was not up to it myself, but I found it and copied it from some web site, though I've since lost that location's address.

@mmcdara I am impressed and astounded that a physics problem can be solved by a completely non-physics approach. Bully for you!

@Rouben Rostamian  Another great reply from you!

From an old list of Harvard weekly problems; with a given mass and a uniform density, this shape produces the greatest gravitational force at the origin.