1 . 椭圆C的中心为坐标原点O,焦点在x轴上,B为上顶点,F为右焦点,若点O到直线BF的距离为焦距的
.
求椭圆C的离心率;
已知直线l不垂直于坐标轴且直线l过点F与椭圆C交于M,N两点,
与
共线.
求直线l的斜率;
设P为椭圆C上任意一点,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb84f6fbac102ccf326b2223d69cb7cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b134e16e6b4d24345b92014d1975b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef244910dcaee5202f4b08dc612bf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c512c047783c07da1d4f4455a4033ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876959b9f90f2379cf3d0927a8e31005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4164b9bee4b6306528ac09a83cef4b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb75be30114a0934ab8d647c4c63a34.png)
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名校
2 . 在平面直角坐标系
中,椭圆
:
的离心率为
,左、右顶点分别为
、
,线段
的长为4.点
在椭圆
上且位于第一象限,过点
,
分别作
,
,直线
,
交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/0eb58f6d-d002-42c5-b828-5e0d0e2cefc1.png?resizew=184)
(1)若点
的横坐标为-1,求点
的坐标;
(2)直线
与椭圆
的另一交点为
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/4ac95fa75e79c870386c9622ce53babe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54638d5d40b56960b252f86b81eb6547.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/0eb58f6d-d002-42c5-b828-5e0d0e2cefc1.png?resizew=184)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd41bad1b506a6f20ea94e41ec4527a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2019-03-08更新
|
966次组卷
|
3卷引用:【市级联考】江苏省扬州市2019届高三第一学期期末检测数学试题
3 . 如图,在平面直角坐标系xOy中,椭圆
过点
,
,其中e为椭圆的离心率,过定点
的动直线l与椭圆交于A,B两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/eec5c8c1-e652-4624-b046-ee8023333f18.png?resizew=199)
求椭圆的方程;
设椭圆的右准线与x轴的交点为M,若
总成立,求m的值;
是否存在定点
其中
,使得
总成立?如果存在,求出点M的坐标
用m表示
;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5787b3d4d9ab6aad4c73a35993e1ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf992e9fc9d23664f7a7b3cd6fbe906f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec9ca77200280c2696202517ef88067.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/eec5c8c1-e652-4624-b046-ee8023333f18.png?resizew=199)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4256bbfa8f3be744a77598a133fe52e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec61d2179863351bfae4e3e8a49cf41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d61c6ddf6afa7d78122fe57df96ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1609bd7022e34f5c4a5b9bc7a9cd87a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00674bab694988593ecbfb918fe9d60d.png)
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4 . 在平面直角坐标系xOy中,椭圆
的左,右焦点分别为
,
,上顶点为A,射线
交椭圆于
若
的面积为
,内角A为
,则椭圆的焦距为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.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/78aa834961df10c8bc3c64615fb79f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2639ce6b7c38975bcbd7c2d9814da324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1086bf902062562c198032cbcbb7faf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f26a1fa02b66554d41b65249601610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe8dc472dade6cea6943164792ab532.png)
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5 . 在平面直角坐标系xOy中,已知椭圆C:
的右准线方程为
,右顶点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/da6bc8c4-706a-46f4-bc5e-d34908dbf4f0.png?resizew=522)
求椭圆C的方程;
若M,N是椭圆C上不同于A的两点,点P是线段MN的中点.
如图1,若
为等腰直角三角形且直角顶点P在x轴上方,求直线MN的方程;
如图2所示,点Q是线段NA的中点,若
且
的角平分线与x轴垂直,求直线AM的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d125266f7bffeb5292742d81fd65432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc1e1baa04cd44c3e7189624485be71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8850ca88266a65c7d289ebfbea3fe30.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/da6bc8c4-706a-46f4-bc5e-d34908dbf4f0.png?resizew=522)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c218207b973df53ac82516243256e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397c5fcd765e0c0789b2b4350e9970cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa96db3d25760bd718fbbc6856f5a23d.png)
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6 . 已知椭圆C:
的右焦点为
,F关于直线
的对称点Q在椭圆C上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7d35535919c91ba8a9ecea371d22d1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d125266f7bffeb5292742d81fd65432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075c5ae12b67f8d30dedd1a271843a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc9e59eb5bdf71bc47c09eea8c3845e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7d35535919c91ba8a9ecea371d22d1.png)
您最近一年使用:0次
7 . 已知椭圆
的长轴长为
,离心率为
.
![](https://img.xkw.com/dksih/QBM/2019/2/15/2141245377748992/2141374092107776/STEM/98880955e0f64b3ea1629254cc4a7854.png?resizew=238)
(1)求椭圆
的方程;
(2)过动点
的直线交
轴于点
,交椭圆
于点
,
(
在第一象限),且
是线段
的中点.过点
作
轴的垂线交椭圆
于另一点
,延长
交椭圆
于点
.
①设直线
、
的斜率分别为
,证明
为定值;
②求直线
斜率取最小值时,直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://img.xkw.com/dksih/QBM/2019/2/15/2141245377748992/2141374092107776/STEM/98880955e0f64b3ea1629254cc4a7854.png?resizew=238)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8a5982a53874dd3e97d9af6d7942ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a2cc28a0fc418c4edbd702190dd77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21451f7a858408ce47fee33c798ba9d5.png)
②求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
您最近一年使用:0次
8 . 在平面直角坐标系xOy中,已知椭圆C:
的离心率为
,右准线方程为
.
求椭圆C的标准方程;
已知斜率存在且不为0的直线l与椭圆C交于A,B两点,且点A在第三象限内
为椭圆C的上顶点,记直线MA,MB的斜率分别为
,
.
若直线l经过原点,且
,求点A的坐标;
若直线l过点
,试探究
是否为定值?若是,请求出定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9c6fe12d3a9727e00ef87a630302ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14022ea10959145b0baf461071e3ec24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6151cd412893ea25b4e599601bfb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f375dc5addedc5f9fbb72d566939c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731f980ccb6f902d460d0ea2920bfe2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c512c047783c07da1d4f4455a4033ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c92ece1ba3a8c39e0f6aea221b96db6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876959b9f90f2379cf3d0927a8e31005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d914fca886d411979f1f9c08561a8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5117784d5f7629ba7d20788328e6a1cd.png)
您最近一年使用:0次
2019-02-14更新
|
467次组卷
|
2卷引用:【市级联考】江苏省苏州市 2018-2019学年高二第一学期学业质量阳光指标调研卷数学试题
9 . 已知椭圆
过点
,其短轴长的取值范围是
,则椭圆离心率的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0dce10bf671cc2ebc67aa7fd568a9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38620d68461307e424923b903ab518f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8eec1c8d1c199819cc936161dc4a91.png)
您最近一年使用:0次
名校
10 . 已知椭圆
的离心率
,且经过点
,
,
,
,
为椭圆的四个顶点(如图),直线
过右顶点
且垂直于
轴.
(1)求该椭圆的标准方程;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/503814cc-d1fc-4c43-ba25-3729024c1ec8.png?resizew=228)
(2)
为
上一点(
轴上方),直线
,
分别交椭圆于
,
两点,若
,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0348e8cdd04a08e36cf940aa4bbd95b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38398209c6e596145044d5afdea2e80.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求该椭圆的标准方程;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/503814cc-d1fc-4c43-ba25-3729024c1ec8.png?resizew=228)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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5卷引用:【市级联考】江苏省连云港市2018-2019学年高二第一学期期末考试数学试题(理科)
【市级联考】江苏省连云港市2018-2019学年高二第一学期期末考试数学试题(理科)江苏省淮安六校联盟2019-2020学年高三年级第三次学情调查理科数学试题2020届河南省南阳市第一中学高三第九次考试数学(理)试题(已下线)专题02 化繁为简,轻松驾驭解析几何运算有技巧(第五篇)-2020高考数学压轴题命题区间探究与突破江西省瑞金市四校联盟2019-2020学年高三第一次联考试卷数学理科试题