Ans: B
$\left\{\begin{array}{ll}
x-y=0 & \ldots \unicode{x2460} \\
x^2+y^2+6x+ky-k =0 & \ldots \unicode{x2461}
\end{array}\right.$
$\left\{\begin{array}{ll}
x-y=0 & \ldots \unicode{x2460} \\
x^2+y^2+6x+ky-k =0 & \ldots \unicode{x2461}
\end{array}\right.$
Sub. $\unicode{x2460}$ into $\unicode{x2461}$, we have
$\begin{array}{rcl}
x^2+x^2+6x+kx-k & = & 0 \\
2x^2+(6+k)x-k & = & 0
\end{array}$
Since the line and the circle do not intersect with each other, then we have
$\begin{array}{rcl}
\Delta & < & 0\\
(6+k)^2-4(2)(-k) & < & 0 \\
k^2+20k+36 & < & 0 \\
(k+18)(k+2) & < & 0
\end{array}$
Therefore, $-18 < k < -2$.
