The worksheet below mimics some of the construction in the web site https://www.geogebra.org/m/d4k6SjFX.

This seems a crude and limiting way to display a pencil of ellipses tangent in a quadrilateral.

Please provide references (textbooks, articles, etc.) to the mathematics which produces this kind of display.

Pencil_in_quad.mw

Sorry, I was not able to change the displays to inline.

The worksheet below is a failed attempt to produce the display of a pencil of conics tangent to four lines. The worksheet contains an image of the display.

Comments within the worksheet describe the details of the attempt and the solve command which fails.

dhaar provided an answer to a similar question which I posed on November 12 (its web address is in the worksheet) and I hope s(he) will reply to this one as well.

ConicsTangent.mw

The uploaded worksheet contains a copy of figure of a pencil from a geometry book, followed by a failed attempt to code Maple to produce the same figure.

The book containing the figure gives no indication of how to code for the figure. Can the figure be produced in Maple?

Respondents will have to establish their own path to DirectSearch.

Pencil.mw

Please answer the questions posed in the body of the uploaded worksheet.

The worksheet employs the command DirectSearch[SolveEquations]. Responders must establish their own connection to the DirectSearch package.

Invert_Torus.mw

The uploaded worksheet plots conics in polar coordinates.

A circle, parabola and hyperbola all plot correctly, but the plot command for the ellipse displays a shifted circle. What's wrong?

Conic_quandry.mw