X.3

locus of all points:

$❘AX❘=k*❘BX❘,k\in {\mathrm{ℝ}}^{+}$

canonical form:

$\frac{1}{\frac{k^2}{1-k^2}+{\left(\frac{k^2}{1-k^2}\right)}^2}{(x+\frac{k^2}{1-k^2})}^2+\frac{1}{\frac{k^2}{1-k^2}+{\left(\frac{k^2}{1-k^2}\right)}^2}{y}^2=1$

origin and radius:

$r=-\sqrt{\frac{k^2}{1-k^2}+{\left(\frac{k^2}{1-k^2}\right)}^2}$

$x=-\frac{k^2}{1-k^2}$

$y=0$

parameterized form:

$(x+r\cos \varphi ,y+r\sin \varphi ),0\le \varphi \le 2\mathrm{\pi }$