3. A line segment $AB$ of length 4 moves along the positive x-axis, and another line segment $CD$ of length 2 moves along the positive y-axis. If the four endpoints $A$, $B$, $C$, and $D$ are concyclic, then the locus of the center of this circle is $\qquad$
3. $x^{2}-y^{2}=3(x>2, y>1)$.

As shown in Figure 2, let the center of the circle be $M(x, y)(x>2, y>1)$. Then $A(x-2,0)$,
$B(x+2,0)$.
$C(0, y-1)$,
$D(0, y+1)$.
From $|M A|^{2}=|M C|^{2}$,
we get $2^{2}+y^{2}=x^{2}+1^{2}$.
Therefore, the required locus is a segment of a hyperbola, whose equation is $x^{2}-y^{2}=3(x>2, y>1)$.