If equations of two curves in a plane are given as
$$ f(x,y)=0,\, g(x,y)=0,\, $$
what geometric interpretation can be given to the following five derived curves i.e., when seen plotted together in relation to individual $f,g?$
$$ f(x,y - g(x,y)=0,\, \tag1 $$
Particularly if $f,g$ are circles the above represents their radical axis. Next,
$$ f(x,y) + g(x,y)=0,\, \tag2$$
and with parameter $\lambda$
$$ f(x,y)+ \lambda \, g(x,y)=0,\, \tag3$$
$$ f(x,y) \cdot g(x,y)=1,\, \tag4$$
$$\frac{ 2 f(x,y)\cdot g(x,y) } {f(x,y) + g(x,y)}=1. \tag5$$