2. If the point is inside the ellipse $k^{2} x^{2}+y^{2}-4 k x+2 k y+k^{2}-1=0$, then the range of the parameter $k$ is
(A) $|k|>1$
(B) $|k| \neq 1$
(C) $-1<k<1$
(D) $0<|k|<1$
(D)
2.【Analysis and Solution】Points outside the ellipse can be very far from the origin, with the absolute values of their coordinates $x, y$ being very large, making the left side of the equation greater than 0. Therefore, the coordinates of internal points make the left side of the equation less than 0. Substituting the coordinates of the origin into the left side of the equation yields $k^{2}-1<0$. Also, $k \neq 0$ (otherwise the equation does not represent an ellipse), so the answer is (D).