CN-LEAGUE 1996

Connect the commom points of circle $x^2+(y-1)^2=1$ and ellipse $9x^2+(y+1)^2=9$ with line segments, the figure is a $\text{(A)}$ line segment $\text{(B)}$ scalene triangle $\text{(C)}$ equilateral triangle $\text{(D)}$ quadrilateral

For geometrical sequence $(a_n)$ , the first term $a_1=1536$ , common ratio $q=-\frac{1}{2}$ . Let $\pi_n=\prod_{i=1}^n a_i$ , so the lagerest one in $(\pi_n)$ is $\text{(A)} \pi_9 \text{(B)} \pi_{11} \text{(C)} \pi_{12} \text{(D)} \pi_{13}$

For a prime number $p$ , there exists $n\in\mathbb{Z}_+$ , $\sqrt{p+n}+\sqrt{n}$ is an integer, then $\text{(A)}$ there is no such $p$ $\text{(B)}$ there in only one such $p$ $\text{(C)}$ there is more than one such $p$ , but finitely many $\text{(D)}$ there are infinitely many such $p$