1 . 设点
是椭圆
上任意一点,过点
作椭圆的切线,与椭圆
交于
两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ace6602b-ed9b-4579-a1ec-98d61a6294b3.png?resizew=155)
(1)求证:
;
(2)
的面积是否为定值?若是,求出这个定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e91e565e14d96a20169db44fcde58a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ace6602b-ed9b-4579-a1ec-98d61a6294b3.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b0bec6e780130fbed900fdb153555d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2024-02-05更新
|
1469次组卷
|
6卷引用:四川省成都市第七中学2024届高三下学期入学考试数学(文)试题
名校
解题方法
2 . 如图,四边形
为坐标原点
是矩形,且
,
,点
,点
,
分别是
,
的
等分点,直线
和直线
的交点为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6394be09d71c984d3c7cc59978b10e.png)
在同一个椭圆C上,求出该椭圆C的方程;
(2)已知点P是圆
上任意一点,过点P作椭圆C的两条切线,切点分别是A,B,求
面积的取值范围.
注:椭圆
上任意一点
处的切线方程是:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66160b4087eca72e6037e1d741f51750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af50cf2832f5f794166ea50dc1cd4964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97fa227c5cd6f012ee1bde773d3221fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9222b3f4af74557bc8341ab973940ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498434bc7de78b25f4873634ba0ac587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c406c4f1880daebcccf913ba3f93512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3b37020a1975e5133c3971645f2849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac19e2a797cd0a408316988a63b3755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43666d22e30f4f80b9db4a71e420932c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d76e83bb80c2f701fce203e685d51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6394be09d71c984d3c7cc59978b10e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9ccd87a3f146204701371b02ff0dcc.png)
(2)已知点P是圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c283fb57b384c7bbe0911d37eb9cd714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
注:椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa4b9c4ddbe4218edabe94f52267795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/593f6dcaaeb66bdfd77235008149f1f4.png)
您最近一年使用:0次
2024-05-24更新
|
552次组卷
|
2卷引用:四川省成都市第七中学2024届高三下学期5月模拟考试文科数学试题
名校
解题方法
3 . 已知椭圆
的上下顶点分别为
,左右顶点分别为
,四边形
的面积为
,若椭圆
上的点到右焦点距离的最大值和最小值之和为6.
(1)求椭圆
的方程;
(2)过点
且斜率不为0的直线
与
交于
(异于
)两点,设直线
与直线
交于点
,证明:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e5d91f4f631c580c155eba8c92bda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c423cfa71956862edbed10a5ba12d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2024-03-21更新
|
520次组卷
|
2卷引用:四川省宜宾市2024届高三下学期第二次诊断性考试文科数学试卷
名校
解题方法
4 . 已知点
是圆
的动点,过
作
轴,
为垂足,且
,
,记动点
,
的轨迹分别为
,
.
(1)证明:
,
有相同的离心率;
(2)若直线
与曲线
交于
,
,与曲线
交于
,
,与圆
交于
,
,当
时,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8efd7b690113cfc851401e1540ac1132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb8f6c438fe1fc036c92ccd3fa8465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5d3e8de22b4cadd3aacc6b955dbcd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b62adcc036ff4122e642b506d46c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6824ebd7ee7da0bed69bd761dbb762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.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/1e0bd63f55069a3bc870915010b39225.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/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457e56d8aa132b2aad38ecf7e45f1cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34d2c05dd46ab2ac99d32be44a1465c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3c6876c328f7d7a08515e78fdba136.png)
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2024-02-28更新
|
349次组卷
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2卷引用:四川省绵阳市东辰学校2024届高三下学期第二学月考试数学(理科)试题
解题方法
5 . 已知椭圆
的离心率为
,左右顶点分别为A,B,G为C的上顶点,且
的面积为2.
(1)求椭圆C的方程;
(2)过点
的动直线与C交于M,N两点.证明:直线
与
的交点在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc727c642cbc2181476b7dd8eca471e.png)
(1)求椭圆C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
您最近一年使用:0次
6 . 已知椭圆
的左、右焦点分别为
,离心率为
,且经过点
.
(1)求椭圆
的标准方程;
(2)点
是椭圆
上不在
轴上的任意一点,射线
分别与椭圆
交于点
.设
的面积分别为
.求证:
为定值.
![](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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d82387e48eafb286785a21a8d4150f.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/32999438ca3cafa7a01040b6e99cae44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685da152c14c752f7fe4e4333d1ec4dd.png)
您最近一年使用:0次
2024-04-08更新
|
677次组卷
|
3卷引用:四川省百师联盟2024届高三冲刺卷(二)全国卷理科数学试题
7 . 已知椭圆
的左、右顶点分别为
,右焦点为
,过点
且斜率为
的直线
交椭圆
于点
.
(1)若
,求
的值;
(2)若圆
是以
为圆心,1为半径的圆,连接
,线段
交圆
于点
,射线
上存在一点
,使得
为定值,证明:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcb166b53a49e393871bcb14a528792.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/dad2a36927223bd70f426ba06aea4b45.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d846d0c16bda5882bbb8a557de733c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01adc01f96d2957a3806b2a3893ff7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
名校
解题方法
8 . 已知椭圆
过点
两点,椭圆的离心率为
,
为坐标原点,且
.
(1)求椭圆
的方程;
(2)设P为椭圆
上第一象限内任意一点,直线
与y轴交于点M,直线
与x轴交于点N,求证:四边形
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d2c2aef4a4ac15f9172a80b1b79fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a158c72b071561459803ae1b950d22.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设P为椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
您最近一年使用:0次
2023-09-05更新
|
1146次组卷
|
9卷引用:四川省成都市成都外国语学校2024届高三上学期期中数学(理)试题
四川省成都市成都外国语学校2024届高三上学期期中数学(理)试题四川省成都市成都外国语学校2024届高三上学期期中数学(文)试题安徽省安庆市第一中学2022届高三第三次模拟考试文科数学试题安徽省安庆市第一中学2022届高三第三次模拟考试理科数学试题 (已下线)第08讲 直线与圆锥曲线的位置关系(练习)(已下线)重难点突破16 圆锥曲线中的定点、定值问题 (十大题型)-1(已下线)专题11 圆锥曲线(4大易错点分析+解题模板+举一反三+易错题通关)(已下线)模块三 专题5 大题分类练(解析几何)拔高能力练(已下线)信息必刷卷05(江苏专用,2024新题型)
9 . 已知点
,
,动点
满足直线
与
的斜率之积为
.记动点
的轨迹为曲线
.
(1)求曲线
的方程,并说明
是什么曲线;
(2)设
,
为曲线
上的两动点,直线
与直线
的斜率乘积为
.
①求证:直线
恒过一定点;
②设
的面积为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd3ae7e60bca635e53964d22cdc9369.png)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a551505ae42b49904bab59b17012d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2023-06-03更新
|
409次组卷
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2卷引用:四川省成都市石室中学2023届高考适应性考试(二)文科数学试题
10 . 已知椭圆
过点
,离心率
.
(1)求椭圆C的方程;
(2)设过点A的直线l交椭圆C于另一点B,若△OAB的面积为2,其中O为坐标原点,求直线l的方程;
(3)设过点
的直线l交椭圆C于点M,N,直线MA,NA分别交直线
于点P,Q.求证:线段PQ的中点为定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfaba0309c471a4246ca3254a3cdaf17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
(1)求椭圆C的方程;
(2)设过点A的直线l交椭圆C于另一点B,若△OAB的面积为2,其中O为坐标原点,求直线l的方程;
(3)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17905988258f795b4eb172b19ad2d7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
您最近一年使用:0次
2023-10-26更新
|
1200次组卷
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5卷引用:四川省成都市石室阳安中学2023-2024学年高三上学期11月月考文科数学试题