Solution
= Solution
The <Euclidean distance> is $D(x,y)=\sqrt{x^2+y^2}$. Along the <parametric curve>,
$$
D^2=a^2\cosh^2t+b^2\sinh^2t
=a^2+(a^2+b^2)\sinh^2t.
$$
This is at least $a^2$, with equality exactly when $t=0$. Therefore
$$
\boxed{(x_m,y_m)=(a,0),\qquad D_{\min}=a}.
$$