maxman105
幼苗
共回答了19个问题采纳率:89.5% 举报
(Ⅰ)椭圆
![](https://img.yulucn.com/upload/1/f0/1f0b27284419d0cbf55597d7521ad960_thumb.jpg)
的右焦点
![](https://img.yulucn.com/upload/5/06/506206a7fd3ef0897000e2730d4d781c_thumb.jpg)
,由题意知
![](https://img.yulucn.com/upload/5/36/5362df84fc4b7cf24fa8b532cde8e6a6_thumb.jpg)
∴
![](https://img.yulucn.com/upload/1/fb/1fb41a48bd242de00328f5359a752924_thumb.jpg)
.……2分
抛物线的标准方程为
![](https://img.yulucn.com/upload/7/62/76267c6c1c8e958f94a44a4012eaee93_thumb.jpg)
.……………………………………………………3分
(Ⅱ)解法一:设直线
![](https://img.yulucn.com/upload/b/a3/ba315cde91fd2b5a1b73a38c7f53ec63_thumb.jpg)
方程为
![](https://img.yulucn.com/upload/8/6f/86f6b31405c9182f3c953386458394f6_thumb.jpg)
,
![](https://img.yulucn.com/upload/f/96/f96bfcde968edf3b3d12af4718f871e1_thumb.jpg)
.
由
![](https://img.yulucn.com/upload/1/98/1986fe51e70bbbd96726bd166f98cb51_thumb.jpg)
得
![](https://img.yulucn.com/upload/7/01/701ca66067e47a3aa930be27fd3f70bb_thumb.jpg)
.…………………………………4分
则
![](https://img.yulucn.com/upload/2/a0/2a0a3e402226d24c23333d00091a9fb3_thumb.jpg)
.…………………………………………………5分
∵
![](https://img.yulucn.com/upload/9/49/949ea40e59d2c1d1453d60d8ecef9c94_thumb.jpg)
⊥
![](https://img.yulucn.com/upload/9/71/9712ad6d30fb31cb3f3a2d652b7d8d3e_thumb.jpg)
,
![](https://img.yulucn.com/upload/1/d6/1d604469e9fdd60ec28cd2230adaa334_thumb.jpg)
,
∴
![](https://img.yulucn.com/upload/e/c4/ec4e24c3bfaabcf16a2b5f860aaaecb2_thumb.jpg)
,∴
![](https://img.yulucn.com/upload/a/fb/afb03fcc6c38e1361290be667dae25ad_thumb.jpg)
.……………………
![](https://img.yulucn.com/upload/7/29/729f6d6ac7ede25969ae8ece8e87a973_thumb.jpg)
……………7分
∴直线
![](https://img.yulucn.com/upload/b/a3/ba315cde91fd2b5a1b73a38c7f53ec63_thumb.jpg)
的方程为
![](https://img.yulucn.com/upload/3/7e/37ea121eef4bc5b98c97ed34a814694a_thumb.jpg)
,该直线恒过定点
![](https://img.yulucn.com/upload/6/99/699cbbb37b4c103e83d38d1ac2b3b713_thumb.jpg)
0 .……………………8分
解法二:①当直线
![](https://img.yulucn.com/upload/b/a3/ba315cde91fd2b5a1b73a38c7f53ec63_thumb.jpg)
的斜率不存在时,易求直线
![](https://img.yulucn.com/upload/b/a3/ba315cde91fd2b5a1b73a38c7f53ec63_thumb.jpg)
的方程为
![](https://img.yulucn.com/upload/a/8e/a8ed17390096207d7dce5b92d86c7956_thumb.jpg)
,
直线
![](https://img.yulucn.com/upload/b/a3/ba315cde91fd2b5a1b73a38c7f53ec63_thumb.jpg)
过定点
![](https://img.yulucn.com/upload/8/12/812e790e17d79c96af575ab6ca759b86_thumb.jpg)
. ……………………………………………………………4分
②当直线
![](https://img.yulucn.com/upload/b/a3/ba315cde91fd2b5a1b73a38c7f53ec63_thumb.jpg)
的斜率存在时,设直线
![](https://img.yulucn.com/upload/b/a3/ba315cde91fd2b5a1b73a38c7f53ec63_thumb.jpg)
的方程为:
![](https://img.yulucn.com/upload/4/65/4655060fe1759c22d374fccb97e21ccc_thumb.jpg)
,
由
![](https://img.yulucn.com/upload/7/89/7893129cede0a32886f68aed4f028466_thumb.jpg)
得
![](https://img.yulucn.com/upload/5/49/549c4b2b34c563d279721c7415c652f3_thumb.jpg)
.
则
![](https://img.yulucn.com/upload/2/d9/2d9dd4264bcdfd089429726cc808c06d_thumb.jpg)
.………………………………………………5分
∵
![](https://img.yulucn.com/upload/9/49/949ea40e59d2c1d1453d60d8ecef9c94_thumb.jpg)
⊥
![](https://img.yulucn.com/upload/9/71/9712ad6d30fb31cb3f3a2d652b7d8d3e_thumb.jpg)
,
![](https://img.yulucn.com/upload/1/d6/1d604469e9fdd60ec28cd2230adaa334_thumb.jpg)
,
![](https://img.yulucn.com/upload/e/ba/ebaae8e5458f16d4d60fc0f040de2ba4_thumb.jpg)
,∴
![](https://img.yulucn.com/upload/f/5c/f5cf8eb90e69641bcd83aa0dc2fce128_thumb.jpg)
.…………
1年前
6