1 . 在平面直角坐标系xOy中,已知椭圆
1(a>b>0)的右顶点为(2,0),离心率为
,P是直线x=4上任一点,过点M(1,0)且与PM垂直的直线交椭圆于A,B两点.
(1)求椭圆的方程;
(2)若P点的坐标为(4,3),求弦AB的长度;
(3)设直线PA,PM,PB的斜率分别为k1,k2,k3,问:是否存在常数λ,使得k1+k3=λk2?若存在,求出λ的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22ecb9b0a87ab5098571bdf80441231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9c6fe12d3a9727e00ef87a630302ab.png)
(1)求椭圆的方程;
(2)若P点的坐标为(4,3),求弦AB的长度;
(3)设直线PA,PM,PB的斜率分别为k1,k2,k3,问:是否存在常数λ,使得k1+k3=λk2?若存在,求出λ的值;若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/eb1974fb-db6a-48a0-afa4-a1daf1e0d139.png?resizew=235)
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2 . 点M是棱长为6的正方体
的内切球O球面上的动点,点N为
上一点,
,
,则动点M运动路线的长度为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/94e4d7c5-02e7-40de-8889-02056c927bcc.png?resizew=179)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f23a20779cbf15d4300ffc69f27f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e54038fa9518fc9a3aa2cb97a74196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3515d2d64577cae922236ed8e2ccd39c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d3505c92b870c0dea9d9e8575f7523.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/94e4d7c5-02e7-40de-8889-02056c927bcc.png?resizew=179)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 在平面直角坐标系
中,椭圆
:
(
)的离心率为
,焦点到相应准线的距离为
,动直线l与椭圆交于
两点.
(1)求椭圆
的标准方程;
(2)若
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2981bf2261343f905ec1b5355a3c4.png)
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2020-03-26更新
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712次组卷
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2卷引用:2019届江苏省无锡市第一中学高三下学期2月期初考试数学试题
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4 . 已知椭圆
:
,离心率
,
是椭圆的左顶点,
是椭圆的左焦点,
,直线
:
.
(1)求椭圆
方程;
(2)直线
过点
与椭圆
交于
、
两点,直线
、
分别与直线
交于
、
两点,试问:以
为直径的圆是否过定点,如果是,请求出定点坐标;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ca3af229875348fb4ae2854fdbc466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/411461db15ee8086332c531e086c40c7.png)
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2019-03-24更新
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4卷引用:【全国百强校】江苏省扬州中学2019届高三4月考试数学试题
19-20高二上·江苏·阶段练习
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5 . 过点
的直线
与椭圆
交于
两点,若
则直线
的斜率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1102279358cee3e583d652b2cff852d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff84ae2da2c81b5c7ccb7e52b40eff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2019-11-19更新
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1068次组卷
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3卷引用:江苏省如皋市2019-2020学年度高二年级上学期教学质量调研(一)数学试题
(已下线)江苏省如皋市2019-2020学年度高二年级上学期教学质量调研(一)数学试题江苏省南通巿2019-2020学年高二上学期第一次教学质量调研数学试题安徽省安庆市怀宁中学2019-2020学年高二上学期第二次月考数学(理)试卷
19-20高二上·江苏·阶段练习
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6 . 已知椭圆
经过点
,
是
的一个焦点,过
点的动直线
交椭圆于
两点.
(1)求椭圆
的方程;
(2)是否存在定点
(异于点
),对任意的动直线
(斜率存在)都有
,若存在求出点
的坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c925b1e900666c0f0bae16a83a274d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07bbc46415ec136f5ea9a15f4678bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5421a28dc3675ae20190d6090793246e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)是否存在定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8bb6b44dc190180e1b4aa4df4bc5af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2019-11-06更新
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1021次组卷
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3卷引用:江苏省如皋市2019-2020学年度高二年级上学期教学质量调研(一)数学试题
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7 . 已知抛物线
的焦点为
,点
在抛物线
上,
,且
.
(1)求抛物线
的标准方程;
(2)过点
作直线
,
分别交抛物线
于
,
两点,若直线
,
的倾斜角互补,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4758fcb2f4a4a0011ab0ad7e3ba013e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088f178d36f9c33002e869e6a4ebb489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b27d227ae0542e632a26a7d55e56f0.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbcf0320d94734aedd3d4e2e31b9827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2019-10-14更新
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1062次组卷
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2卷引用:江苏省南通市海安市海安高级中学2019-2020学年高二上学期期中数学试题
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8 . 已知双曲线C的方程是:
(
,
),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
A.当![]() ![]() |
B.过双曲线C右焦点F的直线与双曲线只有一个交点的直线有且只有2条; |
C.过双曲线C右焦点F的直线与双曲线右支交于M,N两点,则此时线段![]() |
D.双曲线C与双曲线:![]() ![]() ![]() |
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9 . 在长方体
中,已知底面
为正方形,
为
的中点,
,
,点
为正方形
所在平面内的一个动点,且满足
,则线段
的长度的最大值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db57eca2a7cbd91bc57372592580a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4a01292ba9b86837acd691c1c9384f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
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2019-06-05更新
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906次组卷
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16卷引用:【市级联考】江苏省南通市2019届高三适应性考试数学试题
【市级联考】江苏省南通市2019届高三适应性考试数学试题(已下线)2018年高三二轮复习测试专项 【苏教版数学】专题七 立体几何四川省成都市双流区棠湖中学2018-2019学年高二上学期期末数学(理)试题四川省遂宁市2017-2018学年高二上学期期末考试数学理试题四川省遂宁市2017-2018学年高二上学期期末考试数学文试题四川省遂宁市2017-2018学年高二上学期教学水平监测数学(理)试题四川省遂宁市2017-2018学年高二上学期教学水平监测数学(文)试题四川省棠湖中学2018-2019学年高二上学期期末考试数学(理)试题江西省南昌市安义中学2019-2020学年高二上学期期末数学(理)试题(已下线)专题27 直线与圆的综合应用-2四川省眉山市2022-2023学年高二上学期期末教学质量检测理科数学试题四川省眉山市2022-2023学年高二上学期期末数学(理)试题(已下线)专题8-1 直线与圆归类(讲+练)-2四川省射洪中学校2022-2023学年高二上学期1月月考数学(理)试题四川省成都经济技术开发区实验中学校2023-2024学年高三上学期10月月考数学(理)试题(已下线)专题1 超级名圆 性质优先 讲
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解题方法
10 . 已知椭圆
的左右焦点分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84d316b10430afac5b0c065f31e1b2c.png)
,上顶点为B,离心率为e,点P在椭圆上(异于点B).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b021f21c-8786-4848-8971-fc37ef43da6a.png?resizew=162)
(1)若椭圆C经过点
及
,求
的取值范围;
(2)记直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c12279880baa3b90297797bf4d29a265.png)
的斜率分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c87cef1d0bd8b2ee3476a5fa4dbbdc7.png)
,若
,且
,求椭圆C的离心率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84d316b10430afac5b0c065f31e1b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b021f21c-8786-4848-8971-fc37ef43da6a.png?resizew=162)
(1)若椭圆C经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c3988d58a90ce85be4e65c4a86de45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12604a5a6371ddb77722d04006f5d5eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b51ba4eb57c3dad6a9356d4b70dc384.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c12279880baa3b90297797bf4d29a265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e02c09428538ce8ae136cff26d3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c87cef1d0bd8b2ee3476a5fa4dbbdc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf1ac7607f9d0a1639ec59757aca5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad7dcfc3e70b0b4c3c93136252b9037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db821941a51ba432ffad4ba5cb253cfc.png)
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