Suppose we are given a positive number $k$ and a quadrilateral $ABCD$ in which $AB$ and $CD$ are not parallel. Find the locus of points N OUTSIDE $ABCD$ for which $[ABN]- [CDN] = k$.
Note: $[ABN]$ denotes the area of triangle $ABN$.
(You may assume that $ABCD$ is convex for simplicity)
This was given as a "comment" in a book and I was wondering how to prove it. Any help is appreciated, thank you
Updated on 25 March: As requested, please find the piece of the lecture note I have for that part in image here (sorry for late reply as sometimes I am not checking this, fyi):
