2016年5月福州市普通高中毕业班综合测试文科数学试题(word 版含(3)

··········································· 6分 由（Ⅰ）知，DF ·

又因为AB 4，所以PD AD 2，

2016年5月7日福州高三质检文科数学含答案

················································· 7分 所以AP 2AF 2, ·

············································································ 8分 所以 ADP为正三角形， ·

····································································· 9分 所以AO

PD，且AO ·

因为AB 平面PAD，AB//CD，

所以CD 平面PAD． ·············································································· 10分 因为AO 平面PAD， 所以CD AO， ······················································································ 11分 又因为PD CD D，所以AO 平面PCD．

所以三棱锥A

PCD ································································ 12分 （20）本小题考查点与圆、直线与椭圆的位置关系等基础知识，考查运算求解能力、推理论证能力，考查数形结合思想、化归与转化思想等.满分12分．

解法一：

（Ⅰ）依题意得，2c a 4， ···················································· 2分 所以b2 a2 c2 1， ·················································································· 3分

x2

y2 1． ·所以E的方程为····································································· 4分 4

（Ⅱ）点A在 M外．理由如下： ································································ 5分 设P x1,y1 ,Q x2,y2 ，

y k(x 1),由 2得(1 4k2)x2 8k2x 4k2 4 0， ············································ 6分 2

x 4y 4,

所以， ( 8k2)2 4(4k2 1)(4k2 4) 48k2 16 0，

8k24k2 4

所以x1 x2 ，x1x2 . ····························································· 8分

1 4k21 4k2

因为AP x1 2,y1 ,AQ x2 2,y2 ，

所以