A family of rectangular hyperbolas of the form $xy = k$ (e.g. $xy = 2$, $xy = 3$ etc) consists of curves that are neither parallel nor intersect. $k$ is any constant.
Similar families seem to be $xy^2 = k$, $y = e^{(k/x)}$ and so on
$1)$ Is there some other property common to these curves?
$2)$ Can they be regarded as non-Euclidean curves in a plane?