名校
解题方法
1 . 在平面直角坐标系
中,设椭圆
的离心率为
,
,
分别是椭圆的左、右焦点,过
作两条互相垂直的直线
,
,直线
与
交于
,
两点,直线
与
交于
,
两点,且
的周长是
.
(1)求椭圆
的方程;
(2)当
时,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014fb9d469a4b0b8a907ac416ad13585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9c6fe12d3a9727e00ef87a630302ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09a8ac969e5cec3be6abf4ff44c692e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8f64ebec4a71a609204458cc54df82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea5c8fe935beac660eda538e59cd43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8f64ebec4a71a609204458cc54df82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea5c8fe935beac660eda538e59cd43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e46c8b1425138338d06c88544229e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ec3027d89a5c98f29b7a0e70c990d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b188a6a50dad3e47caa46f62ed52ddde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4457e3b494a948e0d98fe8bd0bab534.png)
您最近一年使用:0次
2024-04-22更新
|
869次组卷
|
4卷引用:宁夏回族自治区石嘴山市平罗县平罗中学2023-2024学年高三下学期第五次模拟考试数学(理)试题
2 . 已知椭圆
的离心率
,且点
在椭圆E上,直线
与椭圆E交于不同的两点A,B.
(2)设直线OA,OB的斜率分别为
,证明:
;
(3)设直线l与两坐标轴的交点分别为P,Q,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50bbe873760a74d9aedaafc98fe7e83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451ee8353864dfdb87e3a44eb505f83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e02a893620592d2ab3e3c0bff6529f0.png)
(2)设直线OA,OB的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a778e57014d81a57b823ef7761aec5bd.png)
(3)设直线l与两坐标轴的交点分别为P,Q,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d0b8ae5b933dd37b9311034029a0a17.png)
您最近一年使用:0次
名校
解题方法
3 . 如图所示,由半椭圆
和两个半圆
、
组成曲线
,其中点
依次为
的左、右顶点,点
为
的下顶点,点
依次为
的左、右焦点.若点
分别为曲线
的圆心.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/20/ead0b4aa-035a-461b-8fa8-846ac684efd7.png?resizew=183)
(1)求
的方程;
(2)若过点
作两条平行线
分别与
和
交与
和
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6939602e243cd5662d60d8b53d2d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1cbad6f9e495834f0920e63c0351f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f026d5938eb00a18e9933312b9008a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d96e79ed6d14cb6fc736bcc8fee01d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bdbbfae10ee2d7c2ddf447e481af9e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/20/ead0b4aa-035a-461b-8fa8-846ac684efd7.png?resizew=183)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8add39d0693fd42ebe2fbadb601c47ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1f941c5390ea8f60ec7c27cf3eb41b.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
的左、右焦点分别为
,离心率为
,过左焦点
的直线
与椭圆
交于
两点(
不在
轴上),
的周长为
.
(1)求椭圆
的标准方程;
(2)若点
在椭圆
上,且
为坐标原点),求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453ea8f3a2b85526b54bf453871c3820.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8d68257ba90d0b05303d8d4a7bae33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2afc87067a2c8ee603eb8903bac424a.png)
您最近一年使用:0次
2023-02-14更新
|
664次组卷
|
7卷引用:宁夏中卫市2023届高三二模数学(理)试题
名校
解题方法
5 . 已知椭圆E:
的离心率为
,
,
为其左、右焦点,左、右顶点分别为A,B,过
且斜率为k的直线l交椭圆E于M,N两点(异于A,B两点),且
的周长为8.
(1)求椭圆C的方程;
(2)若P为椭圆上一点,O为坐标原点,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5585a42c8f07ad90b94ace9db3d78994.png)
(1)求椭圆C的方程;
(2)若P为椭圆上一点,O为坐标原点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c922f835c095ce76ccef75e396b1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e6453bd1dd6184452f8df1ec70ae59.png)
您最近一年使用:0次
2022-05-14更新
|
971次组卷
|
5卷引用:宁夏银川一中2022届高三第四次模拟考试数学(理)试题
宁夏银川一中2022届高三第四次模拟考试数学(理)试题宁夏银川一中2022届高三第四次模拟考试数学(文)试题河南省好教育联盟2022届普通高校招生全国统一考试猜题压轴卷(AA)高三理科数学试题(已下线)重难点12五种椭圆解题方法-1(已下线)专题29 弦长问题及长度和、差、商、积问题-1
名校
解题方法
6 . 设椭圆
的左,右焦点分别为
,其离心率为
,且点
在C上.
(1)求C的方程;
(2)O为坐标原点,P为C上任意一点.若M为
的中点,过M且平行于
的直线l交椭圆C于A,B两点,是否存在实数
,使得
?若存在,求
值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e501efaf72113fc8ee3d495004fa980.png)
(1)求C的方程;
(2)O为坐标原点,P为C上任意一点.若M为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d107e77106ff1a9cb76b504bbc99bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79896e6065b6653d41533f0ebb120a4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2022-02-21更新
|
797次组卷
|
18卷引用:宁夏石嘴山市第三中学2019-2020学年高二上学期期末考试数学(理)试题
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