解题方法
1 . 已知椭圆
,一组平行直线的斜率是
.
(1)当它们与椭圆相交时,证明这些直线被椭圆截得的线段的中点在同一条直线上;
(2)这组直线中经过椭圆上焦点的直线与椭圆交于
两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64b7ab668d61bcb8ec6d195c672a81e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(1)当它们与椭圆相交时,证明这些直线被椭圆截得的线段的中点在同一条直线上;
(2)这组直线中经过椭圆上焦点的直线与椭圆交于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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名校
解题方法
2 . 已知椭圆
的一个顶点为
,离心率为
.
(1)求椭圆
的方程;
(2)设过椭圆右焦点的直线
交椭圆于
两点,过原点的直线
交椭圆于
两点.若
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f780f4f03699023b1322a1e002539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设过椭圆右焦点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6114947179bed8c2c86ac078e2f8497f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e03566282ef39ad17821036f228174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d9504760b17443be72b9e7014ac6a4.png)
您最近一年使用:0次
2022-05-29更新
|
892次组卷
|
8卷引用:山东省临沂市罗庄区2019-2020学年高二上学期期中数学试题
山东省临沂市罗庄区2019-2020学年高二上学期期中数学试题江西省宜春市高安市高安中学2019-2020学年高二上学期期中数学(理)试题黑龙江省哈尔滨市第九中学2019-2020学年高二上学期期中数学理试题【区级联考】北京市石景山区2019届高三第一学期期末试卷数学(文)试题【全国百强校】北京市人大附中2019年高考信息卷(三)文科数学试题北京市通州区潞河中学2022届高三三模数学检测试题(已下线)重难点15七种圆锥曲线的应用解题方法-1(已下线)专题29 弦长问题及长度和、差、商、积问题-2
解题方法
3 . 在平面直角坐标系
中,椭圆
的中心为坐标原点,左焦点为
,
为椭圆
的上顶点,且
.
![](https://img.xkw.com/dksih/QBM/2021/11/28/2861184892837888/2861779237961728/STEM/ee7cad7d5d824ff2b1c3232c6e818d32.png?resizew=319)
(1)求椭圆
的标准方程;
(2)已知直线
与椭圆
交于
,
两点,直线
与椭圆
交于
,
两点,且
,如图所示,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8a7d5eb27476d3b132af446ec8b2b6.png)
![](https://img.xkw.com/dksih/QBM/2021/11/28/2861184892837888/2861779237961728/STEM/ee7cad7d5d824ff2b1c3232c6e818d32.png?resizew=319)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26327a0c098eba22bb50c3ffd8a240f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.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/dfb9191cf4cd3c7bbc9840bb5a91a5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.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/495021c7da1c77e6ed1d1dd30e0be7bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c482ddecdf0e96951a02cdbf7042ae5.png)
您最近一年使用:0次
4 . 已知椭圆
(
)的离心率为
,且过点
.
(1)求椭圆的标准方程
(2)分别过椭圆的左、右焦点
、
作两条互相垂直的直线
和
,
与
交于
,
与椭圆交于A,B两点,
与椭圆交于C,D两点
①求证:
;
②求证:
定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
(1)求椭圆的标准方程
(2)分别过椭圆的左、右焦点
![](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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5ceaa0100da5342d6ba8bde4ed67eb.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969a4865b1a12054f60b707fb2ee5d39.png)
您最近一年使用:0次
2021-11-23更新
|
720次组卷
|
3卷引用:山东省济南市历下区山东师范大学附属中学2021-2022学年高二上学期期中数学试题
山东省济南市历下区山东师范大学附属中学2021-2022学年高二上学期期中数学试题云南省玉溪第一中学2023-2024学年高二下学期开学考试数学试卷(已下线)专题44 直线与圆锥曲线的位置关系之定值、定点、共线问题-备战2022年高考数学一轮复习一网打尽之重点难点突破
解题方法
5 . 已知椭圆
经过点
,离心率为
,点O为坐标原点.
(1)求椭圆E的标准方程;
(2)设不与坐标轴平行的直线
与椭圆交于A,B两点,与
轴交于点P,设线段AB中点为M.
(i)证明:直线OM的斜率与直线
的斜率之积为定值;
(ii)如图,当
时,过点M作垂直于
的直线
,交
轴于点Q,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆E的标准方程;
(2)设不与坐标轴平行的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8e1ebc1b3f6e793dd06aac312dc9bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(i)证明:直线OM的斜率与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(ii)如图,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93679e8d1984837c46fbe6b08da1d06d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f600e23b3e90cfa44bf6a3c3fb63a0.png)
![](https://img.xkw.com/dksih/QBM/2016/3/11/1572533424783360/1572533430878208/STEM/8689552a-4d84-4ffe-b141-5fd55833b29c.png?resizew=203)
您最近一年使用:0次