XY = c , Mathematical Solutions

Math:
$XY=c$
Let $X=m(r)$
Let $Y=r(m)$
$c=constant$
m(r) is a function of r, $m={c\over r}$
r(m) is a function of m, $r={c\over m}$

What can mathematically be said about all the solutions to this type of equation? A product of two variables is a constant?

Time for math.

#Math

more later about this brief post,
- mr

Some related work here:
http://www.stumblingrobot.com/2016/02/22/find-the-orthogonal-trajectories-of-the-family-xy-c/

And, example #2 here:

https://proofwiki.org/wiki/Orthogonal_Trajectories/Rectangular_Hyperbolas

&

https://www.math24.net/orthogonal-trajectories-page-2/#example2

Quantized levels might look something like this, however, it must be reviewed:

The Surfer, OM-IV

Ω