真题
名校
1 . 设F是椭圆
的右焦点,且椭圆上至少有21个不同的点
,使
组成公差为 d的等差数列,则d的取值范围为 ________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87caa1abc4e83652eb3cb78c54164196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c908049059e290bb6bc7e922f0da0ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd7b56fc1259660603ae14b0de93af9.png)
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真题
解题方法
2 . 已知
,
分别是椭圆
的左、右焦点
,
关于直线
的对称点是圆
的一条直径的两个端点.
(Ⅰ)求圆
的方程;
(Ⅱ)设过点
的直线
被椭圆
和圆
所截得的弦长分别为
,
.当
最大时,求直线
的方程.
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/09ec1ef1c3364f9f90696e8e48e7de0e.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/9bae5f0ff54c4ddba88562dbfc22ca43.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/c193fa530ad2496994d54be7e861a8f4.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/09ec1ef1c3364f9f90696e8e48e7de0e.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/9bae5f0ff54c4ddba88562dbfc22ca43.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/fe47d5dbe3924cc4a21cd6398011c266.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/6b6a6e37e003456292ff3b0dea079157.png)
(Ⅰ)求圆
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/6b6a6e37e003456292ff3b0dea079157.png)
(Ⅱ)设过点
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/9bae5f0ff54c4ddba88562dbfc22ca43.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/7d57fa0cf6b042d2a6f9947255a82fd1.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/d25bf95594cc4304acb9f6d764d6812e.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/6b6a6e37e003456292ff3b0dea079157.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/411eb6555b1d4e66a8e666bb4027b6c3.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/864e5ec398334c51b45e4e34bd61c70b.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/121489f8a3b1444cb7d8ccd09b368d8c.png)
![](https://img.xkw.com/dksih/QBM/2013/7/17/1571289824362496/1571289829867520/STEM/7d57fa0cf6b042d2a6f9947255a82fd1.png)
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3 . 如图,
为坐标原点,椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a259dddccc3cfe8f81735cd5834785d.png)
的左右焦点分别为
,离心率为
;双曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf1bce17440e83c1b735d2954010a2a.png)
的左右焦点分别为
,离心率为
,已知
,且
.
(1)求
的方程;
(2)过
点作
的不垂直于
轴的弦
,
为
的中点,当直线
与
交于
两点时,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a259dddccc3cfe8f81735cd5834785d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf1bce17440e83c1b735d2954010a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626706e779756baf8f7aa4cd276d2017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e749c051ebeba72d9873b4f31c8ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4aed953f852a8f9eab33645b2078dc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/eb8915cc-1337-4d04-a350-edd99f29bb3a.png?resizew=262)
您最近一年使用:0次
2016-12-03更新
|
6730次组卷
|
6卷引用:2014年全国普通高等学校招生统一考试理科数学(湖南卷)
2014年全国普通高等学校招生统一考试理科数学(湖南卷)四川省成都外国语学校2017-2018学年高二下学期入学考试数学(理)试题(已下线)专题30 圆锥曲线三角形面积与四边形面积题型全归类-2(已下线)重难点突破17 圆锥曲线中参数范围与最值问题(八大题型)重庆市第十八中学2023-2024学年高二上学期12月学习能力摸底数学试题(已下线)专题24 解析几何解答题(理科)-3
4 . 如图,椭圆
的离心率为
,
轴被曲线
截得的线段长等于
的长半轴长.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/4332f70d-10f2-4939-81e0-00cd862ae30d.png?resizew=220)
(1)求
,
的方程;
(2)设
与
轴的交点为 M,过坐标原点O的直线
与
相交于点 A,B,直线MA,MB分别与
相交与D,E.
①证明:
;
②记△MAB,△MDE的面积分别是
.问:是否存在直线
,使得
=
?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e671afd184e7bb84266ab42357ebbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/4332f70d-10f2-4939-81e0-00cd862ae30d.png?resizew=220)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e21402367709de8a3cb28d3444d33a55.png)
②记△MAB,△MDE的面积分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358039a7c6e0004bc430d4ee2d89fe1e.png)
您最近一年使用:0次
2016-12-03更新
|
5552次组卷
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6卷引用:2011年普通高等学校招生全国统一考试理科数学(湖南卷)
2011年普通高等学校招生全国统一考试理科数学(湖南卷)【全国百强校】重庆市第一中学2018-2019学年高二上学期期中考试数学(理)试题【全国百强校】黑龙江省鹤岗市第一中学2018-2019学年高二上学期期末考试数学(理)试题江西省景德镇一中2020-2021学年高二上学期期末考试数学(理)试题(已下线)大题专练训练27:圆锥曲线(求直线方程)-2021届高三数学二轮复习(已下线)专题24 圆锥曲线中的存在性、探索性问题 微点2 圆锥曲线中的探索性问题