Mathematics 133
Comments on Chapter IV of the course notes

This chapter is not covered in the Fall 2020 course, but for the record here are links to the files containing this chapter:
http://math.ucr.edu/~res/math133-2018/geometrynotes04a.f13.pdf 
http://math.ucr.edu/~res/math133-2018/geometrynotes04b.f13.pdf
The following six documents ovelap with the notes but also contain much additional material.
https://math.ucr.edu/~res/math133-2020/pg-all.pdf
This is a more formal and detailed book-length treatment of the material in Chapter IV.
https://math.ucr.edu/~res/progeom/quadrics0.pdf                        https://math.ucr.edu/~res/progeom/quadrics1.pdf                        https://math.ucr.edu/~res/progeom/quadrics2.pdf                        https://math.ucr.edu/~res/progeom/quadrics3.pdf                        https://math.ucr.edu/~res/progeom/quadrics4.pdf
These documents involve more advanced material not covered in this course or its prerequisites (for example, from Math 145A).  They are meant to fill some gaps in the formal detailed notes cited above, but nothing from them is needed to read and understand the latter.
 Speaking of conics and quadrics:
Here is a file on this topic.
http://math.ucr.edu/~res/math133-2020/week8/elltangents.pdf   A proof that there are two tangents to an ellipse passing through a given external point.  The (partial) argument in the file shows how one can use geometric transformations to extend a classical theorem in Euclidean geometry for circles to ellipses whose axes are the usual coordinate axes.  One can use the results in the quadrics files to show that the result extends to all ellipses in the coordinate plane.   This file should be accessible to all students in the course, and a pasive understanding is a good indication of how well the main material of the course has been mastered.