4. 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. $0<|k|<1$
4. D Hint: Let $f(x, y)=k^{2} x^{2}+y^{2}-4 k x+2 k y+k^{2}-1$, then when $p\left(x_{0}, y_{0}\right)$ is inside the ellipse, we have $f\left(x_{0}, y_{0}\right)<0, f(0,0)=k^{2}-1<0,0<|k|<1$.