2. Given that the origin is inside the ellipse $k^{2} x^{2}+y^{2}-4 k x+2 k y+k^{2}-1=0$, the range of the parameter $k$ is
A. $|k|>1$
B. $|k| \neq 1$
C. $-1<k<1$
D. $0<|k|<1$
$k^{2} x^{2}+y^{2}-4 k x+2 k y+k^{2}-1=0 \Rightarrow(k x-2)^{2}+(y+k)^{2}=5$
$\Rightarrow \frac{\left(x-\frac{2}{k}\right)^{2}}{\frac{5}{k^{2}}}+\frac{(y+k)^{2}}{5}=1$, since the origin is inside the ellipse, we have $4+k^{2}<5$ and $k \neq 0 \Rightarrow 0<|k|<1$, so the answer is $D$.