1 . 在平面直角坐标系
中,已知动点
到定点
的距离与到定直线
的距离之比为
.
(1)求动点
的轨迹
的方程;
(2)已知
为定直线
上一点.
①过点
作
的垂线交轨迹
于点
(
不在
轴上),求证:直线
与
的斜率之积是定值;
②若点
的坐标为
,过点
作动直线
交轨迹
于不同两点
,线段
上的点
满足
,求证:点
恒在一条定直线上.
![](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/055a2ef09e2ee0948cf67c58de58732d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
①过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c2293f93791a597bf0162411f3395f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307bd991211ec79b47a4be52933bb8e7.png)
②若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245ad1e79cc6973ab7262f9f0538c71a.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95ccc811dff1bc10c961bfc6ffc70c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0cb4b2e0a7af501779001e4f6bb6c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dd083a474de9b4bce5589f71619f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
您最近一年使用:0次
2 . 已知椭圆C:
,点P
,过右焦点F作与y轴不垂直的直线l交椭圆C于A,B两点.
(Ⅰ )求椭圆C的离心率;
(Ⅱ )求证:以坐标原点O为圆心与PA相切的圆,必与直线PB相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5c3efe5af4e95a7b7b00f7a0092762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e32f16d75ccb62a04970f861827fca.png)
(Ⅰ )求椭圆C的离心率;
(Ⅱ )求证:以坐标原点O为圆心与PA相切的圆,必与直线PB相切.
您最近一年使用:0次
3 . 已知点
是椭圆
的左、右顶点,
为左焦点,点
是椭圆上异于
的任意一点,直线
与过点
且垂直于
轴的直线
交于点
,直线
于点
.
(1)求证:直线
与直线
的斜率之积为定值;
(2)若直线
过焦点
,
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f261904425331ffff68f003dbdb7cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6d8190ce24defed822827b06ec2cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
4 . 如图,已知椭圆
:
的离心率为
,
、
为椭圆的左右顶点,焦点到短轴端点的距离为2,
、
为椭圆
上异于
、
的两点,且直线
的斜率等于直线
斜率的2倍.
![](https://img.xkw.com/dksih/QBM/2017/4/12/1664255895011328/1664742548209664/STEM/1256551cd8094f468ce208fe67e90d1c.png?resizew=249)
(Ⅰ)求证:直线
与直线
的斜率乘积为定值;
(Ⅱ)求三角形
的面积
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://img.xkw.com/dksih/QBM/2017/4/12/1664255895011328/1664742548209664/STEM/1256551cd8094f468ce208fe67e90d1c.png?resizew=249)
(Ⅰ)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
(Ⅱ)求三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1de7da3ab92e70f135ea628a691167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2017-04-13更新
|
897次组卷
|
2卷引用:2017届安徽省宣城市高三下学期第二次调研(模拟)考试数学(理)试卷
名校
5 . 已知椭圆
:
的离心率为
,右焦点为F,点
在椭圆
上.
(Ⅰ)求椭圆
的方程;
(Ⅱ)过点
的直线交椭圆
于
,
两点,交直线
于点
,设
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab82775e95758e01ef5c99a732c55d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)过点
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35539d533bfc4eb3196963a985fc4010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794966f5af14904e0f6e61144bf6e3fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
2017-04-11更新
|
823次组卷
|
3卷引用:2016-2017学年北京市丰台区高三想上学期一模练习理数试卷
2010·江苏盐城·三模
名校
6 . 已知椭圆
:
的左、右焦点分别为
,下顶点为
,点
是椭圆上任一点,⊙
是以
为直径的圆.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/de705bab-d5d6-4b96-9939-65108210b7b2.png?resizew=181)
(Ⅰ)当⊙
的面积为
时,求
所在直线的方程;
(Ⅱ)当⊙
与直线
相切时,求⊙
的方程;
(Ⅲ)求证:⊙
总与某个定圆相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/de705bab-d5d6-4b96-9939-65108210b7b2.png?resizew=181)
(Ⅰ)当⊙
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c487fec20bd809e0baf5cb39afe8979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
(Ⅱ)当⊙
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅲ)求证:⊙
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2019-01-30更新
|
1164次组卷
|
4卷引用:盐城市2009-2010学年度高三年级第三次调研考试数学试卷
(已下线)盐城市2009-2010学年度高三年级第三次调研考试数学试卷安徽省合肥市庐阳区第一中学2019-2020学年高二上学期期末数学(理)试题安徽省合肥市第一中学2019-2020学年高二上学期期末理科数学试题四川省遂宁市第二中学校2023届高三第七次模拟文科数学试题
名校
7 . 已知椭圆
的离心率为
,且过点
.
![](https://img.xkw.com/dksih/QBM/2017/3/19/1647033146163200/1647946590683136/STEM/5e006acb6ced4f3588f675b6613dcbbe.png?resizew=210)
(
)求椭圆
的方程;
(
) 设点
在椭圆
上,且
与
轴平行,过
点作两条直线分别交于椭圆
于两点
,若直线
平分
,求证:直线
的斜率是定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146092f5bcaa4d9f689630aa5b6c051f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45125b093276ec1bb76acce42255d378.png)
![](https://img.xkw.com/dksih/QBM/2017/3/19/1647033146163200/1647946590683136/STEM/5e006acb6ced4f3588f675b6613dcbbe.png?resizew=210)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.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/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](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/b20c15cbb1f383180b4bef7c70485e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2017-03-20更新
|
1006次组卷
|
2卷引用:2017届江苏省如东高级中学高三2月摸底考试数学试卷
名校
8 . 设
、
分别是椭圆
的左、右焦点,
是椭圆
上的点,且
,坐标原点
到直线
的距离是
.
(Ⅰ)求椭圆
的离心率;
(Ⅱ)过椭圆
的上顶点
作斜率为
的直线
交椭圆
于另一点
,点
在椭圆
上,且
,求证:存在
,使得
.
![](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/44be7c7a0fa7feb14a1223f679bfb1ca.png)
![](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/b9d33dd9655686e816a0323a2d2f3112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e140d3e6277b84f6e1de7f670b3817a.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe29f48d3e0f6dd0f449c5cb66ef734.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/ac047e91852b91af639feec23a9598b2.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/12777a96242feadf7964af7823b7450c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1766068ddb626ead2d2c31bcb613b46d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7be191750051c755e1bfc410d883386.png)
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2017-03-09更新
|
940次组卷
|
2卷引用:2017届安徽省宿州市高三第一次教学质量检测(期末)文数试卷
真题
9 . 设
,在平面直角坐标系中,已知向量
,向量
,
,动点
的轨迹为E.
(1)求轨迹E的方程,并说明该方程所表示曲线的形状;
(2)已知
,证明:存在圆心在原点的圆,使得该圆的任意一条切线与轨迹E恒有两个交点A,B,且
(O为坐标原点),并求出该圆的方程;
(3)已知
,设直线
与圆C:
(1<R<2)相切于A1,且
与轨迹E只有一个公共点B1,当R为何值时,|A1B1|取得最大值?并求最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d1dbacb32c6aa64b346cfc40c5e7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069d5e4878e17bf1f2bd494d5f1c8447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc74c79951a73d068aa2229f7d415d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a32a090bc3ff8e2e53407c2ae4084cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
(1)求轨迹E的方程,并说明该方程所表示曲线的形状;
(2)已知
![](https://img.xkw.com/dksih/QBM/2010/3/12/1569631062581248/1569631152578560/STEM/ad66f3538bea4def8499012dccd571f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada5c15d7b42b2fb2836c3478ae5fb34.png)
(3)已知
![](https://img.xkw.com/dksih/QBM/2010/3/12/1569631062581248/1569631152578560/STEM/ad66f3538bea4def8499012dccd571f5.png)
![](https://img.xkw.com/dksih/QBM/2010/3/12/1569631062581248/1569631152578560/STEM/eb968bca05eb47dcb4e86eb45f24c831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d443779a9f5889e921a60e5b452a926f.png)
![](https://img.xkw.com/dksih/QBM/2010/3/12/1569631062581248/1569631152578560/STEM/eb968bca05eb47dcb4e86eb45f24c831.png)
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2019-01-30更新
|
2836次组卷
|
4卷引用:2009年普通高等学校招生全国统一考试文科数学(山东卷)
2009年普通高等学校招生全国统一考试文科数学(山东卷)(已下线)2012-2013学年四川省外语实验学校高二4月数学试卷高中数学解题兵法 第三十四讲 分类讨论是一种重要的解题策略(已下线)专题23 圆锥曲线中的最值、范围问题 微点1 圆锥曲线中的最值问题
解题方法
10 . 设
是椭圆
的左、右焦点,
是椭圆
上任意一点.
(1)记
,求证:
;
(2)若
,点
,已知椭圆
上的两个动点
满足
,当
时,求直线
斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6f95c70af169c4af991af8c5e3c0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa4ae8d7537feb98c7de50302705609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ab53d020bf8f3afcec53fc38f64f6c9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12796b93f8489abab501f6896d5359dc.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/86050930230676a4eb344c0c734acc6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a29226a0a98dce2a2353e9214a901f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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