名校
1 . 给定椭圆
,称圆
为椭圆
的“伴随圆”.已知点
是椭圆
上的点
(1)若过点
的直线
与椭圆
有且只有一个公共点,求
被椭圆
的伴随圆
所截得的弦长:
(2)
是椭圆
上的两点,设
是直线
的斜率,且满足
,试问:直线
是否过定点,如果过定点,求出定点坐标,如果不过定点,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c25dc383b1f771c104e2db89a00562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179fe7eff7abfdd092b63c9c1b82d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef0fff05202a55ead6e4bf9c9ef3ebc.png)
(1)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e717e7c65d8875194aed1eddef22978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d02480d96ca25d089353a24d93f20a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
您最近一年使用:0次
2018-03-08更新
|
1147次组卷
|
4卷引用:江苏省盐城中学2018届高三上学期期末考试数学试题2
江苏省盐城中学2018届高三上学期期末考试数学试题2【全国百强校】湖南省衡阳市第八中学2017-2018学年高二下学期期末结业考试数学(理)试题【校级联考】天津市六校联考(静海一中、杨村一中、宝坻一中等)2018届高三(上)期末模拟考试数学(理)试题(已下线)2017-2018学年度下学期高一数学期末备考总动员C卷
2 . 已知椭圆
的离心率为
,
分别为椭圆的左,右焦点,
分别为椭圆的左,右顶点,D为椭圆的上顶点.原点
到直线
的距离为
.设点
在第一象限,其纵坐标为t,且
轴,连接
交椭圆于点
.
![](https://img.xkw.com/dksih/QBM/2018/2/19/1885838201839616/1889157694980096/STEM/55ad4ad555ce44efa602e2a4b91c49d3.png?resizew=237)
(1)求椭圆
的方程;
(2)若三角形
的面积等于四边形
的面积,求直线
的方程;
(3)求过点
的圆方程(结果用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd40fadf77c01c856c9e5848c4215fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/465aec2e55491394d6a8bfa3ffb2b833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/2018/2/19/1885838201839616/1889157694980096/STEM/55ad4ad555ce44efa602e2a4b91c49d3.png?resizew=237)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f7c674f87a67fde99afceb3cfd8189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
(3)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738bdf8950e432d335af5379f61a2dbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
3 . 已知左、右焦点分别为
的椭圆
与直线
相交于
两点,使得四边形
为面积等于
的矩形.
(1)求椭圆
的方程;
(2)过椭圆
上一动点
(不在
轴上)作圆
的两条切线
,切点分别为
,直线
与椭圆
交于
两点,
为坐标原点,求
的面积
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ef6f0e1585b02d72fa399ce262f915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e87937025a66487fa6bac61fa30ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c29a7e8eea08197bf53164a560bee58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01882f77f211b5b82111bc2953f01d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ff2fcfb0f38d9ef48254703fa336bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1543dcb234e0ec92e1dc2ee59692a18.png)
您最近一年使用:0次
2017-11-16更新
|
3290次组卷
|
6卷引用:江苏省徐州市三校联考2020-2021学年高三上学期期末数学试题
江苏省徐州市三校联考2020-2021学年高三上学期期末数学试题河北省石家庄市第二中学2018届高三12月月考数学(理)试题河北省实验中学2021届高三上学期期中数学试题(已下线)专题7 圆锥曲线之极点与极线 微点1 圆锥曲线之极点与极线(已下线)第五篇 向量与几何 专题4 极点与极线 微点1 圆锥曲线之极点与极线(一)四川省成都市第七中学2017-2018学年高二上学期半期考试数学(理)试题
解题方法
4 . 已知椭圆
的上顶点为
,直线
交椭圆于
两点,设直线
的斜率分别为
.
![](https://img.xkw.com/dksih/QBM/2015/3/25/1572028403212288/1572028409102336/STEM/a70389427e90425682cff9b9a5aa10e9.png?resizew=189)
(1)若
时,求
的值;
(2)若
时,证明直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://img.xkw.com/dksih/QBM/2015/3/25/1572028403212288/1572028409102336/STEM/a70389427e90425682cff9b9a5aa10e9.png?resizew=189)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257beb71337358f5ccc57219d9153666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
您最近一年使用:0次
2016-12-03更新
|
796次组卷
|
2卷引用:2015届江苏省无锡市高三上学期期末考试理科数学试卷
10-11高三·江苏常州·期末
名校
解题方法
5 . 在平面直角坐标系
中,椭圆
:
的右焦点为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a36aeca2ba23ce5bc2dab928158e62.png)
(
,
为常数),离心率等于0.8,过焦点
、倾斜角为
的直线
交椭圆
于
、
两点.
⑴求椭圆
的标准方程;
⑵若
时,
,求实数
;
⑶试问
的值是否与
的大小无关,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4c9d22ff6c1bb58c4313a40018d612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a36aeca2ba23ce5bc2dab928158e62.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ee36f4cdcef902aa4fa3905cb35dde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ab55147ca5c0f958af43b0637ee31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
⑴求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
⑵若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bbc6c821f7ab0bfc267a6c5061996f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386406e5437aac324d647f51b8b2e5eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
⑶试问
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d92c510c7a614077d2c1cf5f6ce190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ab55147ca5c0f958af43b0637ee31b.png)
![](https://img.xkw.com/dksih/QBM/2011/2/10/1569982764883968/1569982770143232/STEM/f1b1d47c672c4b64bdb8a265db2d5cf1.png)
您最近一年使用:0次
2016-12-02更新
|
2346次组卷
|
6卷引用:2011届江苏省常州市教育学会高三学生学业水平监测数学试卷
(已下线)2011届江苏省常州市教育学会高三学生学业水平监测数学试卷2019届江苏省淮安市淮阴中学高三下学期4月高考模拟数学试题(已下线)2014届高考数学总复习考点引领+技巧点拨第九章第11课时练习卷2015-2016学年江苏省泰兴市一中高二上学期期中考试数学试卷(已下线)专题13 极坐标秒解圆锥曲线 微点1 极坐标秒解圆锥曲线(已下线)2012-2013学年湖北武汉部分重点中学高二下学期期中考试文数学试卷
2010·北京·二模
解题方法
6 . 已知椭圆
和圆
:
,过椭圆上一点P引圆O的两条切线,切点分别为A,B.
![](https://img.xkw.com/dksih/QBM/2013/6/28/1571259842387968/1571259847589888/STEM/a69117e79c5548af95ff12f69faa99e1.png?resizew=328)
(1)(ⅰ)若圆O过椭圆的两个焦点,求椭圆的离心率e的值;
(ⅱ)若椭圆上存在点P,使得
,求椭圆离心率e的取值范围;
(2)设直线AB与x轴、y轴分别交于点M,N,问当点P在椭圆上运动时,
是否为定值?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4ab88bc995ac5fc57518930a03c534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://img.xkw.com/dksih/QBM/2013/6/28/1571259842387968/1571259847589888/STEM/a69117e79c5548af95ff12f69faa99e1.png?resizew=328)
(1)(ⅰ)若圆O过椭圆的两个焦点,求椭圆的离心率e的值;
(ⅱ)若椭圆上存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df9b574c6b6a4c878bf425d4fa31d66.png)
(2)设直线AB与x轴、y轴分别交于点M,N,问当点P在椭圆上运动时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad3e95a9b0223e280a9034a91b29fbc.png)
您最近一年使用:0次