$26 \cdot 4$ If the curve $x^{2} \cos \alpha-y^{2} \sin \alpha+2=0$ is an ellipse, then the center of the circle $(x+\cos \alpha)^{2}+$ $(y+\sin \alpha)^{2}=1$ is in
(A) the first quadrant.
(B) the second quadrant.
(C) the third quadrant.
(D) the fourth quadrant.
(China Sichuan Province High School Mathematics Competition, 1990)
［Solution］The equation of the ellipse can be transformed into $y^{2} \sin \alpha-x^{2} \cos \alpha=2$. Since it is an ellipse, then $\sin \alpha>0$, and $\cos \alpha<0$, which means $\alpha$ is in the second quadrant. Given that the center of the circle is at $(-\cos \alpha,-\sin \alpha)$, it is located in the fourth quadrant. Therefore, the answer is $(D)$.