Ans: D
$\left\{\begin{array}{ll}
x^2 + y^2 -6x + cy -7 =0 & \ldots \unicode{x2460} \\
x-y +9=0 & \ldots \unicode{x2461}
\end{array}\right.$
$\left\{\begin{array}{ll}
x^2 + y^2 -6x + cy -7 =0 & \ldots \unicode{x2460} \\
x-y +9=0 & \ldots \unicode{x2461}
\end{array}\right.$
From $\unicode{x2461}$, we have
$\begin{array}{rcl}
x – y + 9 & = & 0 \\
y & = & x + 9 \ldots \unicode{x2462}
\end{array}$
Sub. $\unicode{x2462}$ into $\unicode{x2460}$, we have
$\begin{array}{rcl}
x^2 + (x+9)^2 -6x +c(x+9) – 7 & = & 0 \\
x^2 + x^2 +18x + 81 – 6x +cx +9c -7 & = & 0 \\
2x^2 + (12 + c)x + 74 +9c & = & 0
\end{array}$
For the circle and the straight line intersect,
$\begin{array}{rcl}
\Delta & \ge & 0 \\
(12+c)^2 – 4\times 2 \times (74 +9c) & \ge & 0 \\
144 + 24c +c^2 -592 – 72c & \ge & 0 \\
c^2 -48c -448 & \ge & 0 \\
(c – 56)(c+8) & \ge & 0
\end{array}$
Therefore, $c \le -8$ or $c \ge 56$.
