3. The necessary and sufficient condition for the focal distance of the curve $\frac{x^{2}}{16-k}-\frac{y^{2}}{k}=1$ to be equal to that of the curve $9 x^{2}+25 y^{2}=225$ is
A. $k0$, and $k \neq 16$
C. $016$
3. A Prompt: The focal distance of the ellipse $9 x^{2}+25 y^{2}=225$ is 8. Clearly $k \neq 0$. When $k<0$, it represents an ellipse, with a focal distance of $2 \sqrt{(16-k)+k}=2 \sqrt{16}=8$; similarly, when $0<k<16$, the equation represents a hyperbola, with a focal distance of 8 as well.