选 C因p>0,A、B是切点,切线过(0,-1/2)设A(a,a²/(2p)),B(b,b²/(2p)),a>0,b<0y'=x/pA处切线斜率k=a/p,切线方程ax-py-a²/2=0它过(0,-1/2)得:0+p/2-a²/2=0a=√p,A(√p,1/2)同理:b=-√p,B(-√p,1/2)直线AB方程:y=1/2,它过焦点F(0,p/2),得 p=1抛物线方程:x²=2y所以 选C
