[tex]\{x,y\}i.p.\{2,3\}\Rightarrow \dfrac{x}{\frac{1}{2}}=\dfrac{y}{\frac{1}{3}}=k\Rightarrow x=\dfrac{k}{2},y=\dfrac{k}{3}\\
x^2+y^2=208\\
\dfrac{k^2}{4}+\dfrac{k^2}{9}=208|\cdot 36\\
9k^2+4k^2=7488\\
13k^2=7488\\
k^2=576\Rightarrow k\in \{\pm 24\}\\
Pt.\ k=24\Rightarrow (x,y)=(12,8)\\
Pt.\ k=-24\Rightarrow (x,y)=(-12,-8)\\
S:(x,y)\in \{(12,8);(-12,-8)\}[/tex]
