14. (15 points) Given positive real numbers $x, y$ satisfy
$$
\begin{array}{l}
a=x+y, \\
b=\sqrt{x^{2}+7 x y+y^{2}} .
\end{array}
$$
(1) When $y=1$, find the range of $\frac{b}{a}$;
(2) If $c^{2}=k x y$, and for any positive numbers $x, y$, the segments with lengths $a, b, c$ can always form a triangle, find the range of $k$.