名校
解题方法
1 . 焦距为
的椭圆
(
)满足
、
、
成等差数列,称
为“等差椭圆”.
(1)求
的离心率;
(2)过
作直线
与
有且只有一个公共点,求此直线的斜率
的值;
(3)设点
为椭圆的右顶点,
为椭圆上异于
点的任一点,
为
关于原点
的对称点(
也异于
),直线
、
分别与
轴交于
、
两点,判断以线段
为直径的圆是否过定点?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dcc91c2ffb5571eaf944c34f5e8ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee90e546232d08bb57108f2d5f87439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cfedfa5cc6b32402e5388c012ef61dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设点
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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)
您最近一年使用:0次
2 . 已知
, 如图, 曲线
由曲线
和曲线
组成,其中点
为曲线
所在圆锥曲线的焦点, 点
, 为曲线
所在圆锥曲线的焦点
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/21/a745d57c-7346-4f2f-983d-c82aee968e6d.png?resizew=251)
(1)若
, 求曲线
的方程;
(2)如图, 作斜率为正数的直线
平行于曲线
的渐近线, 交曲线
于点
, 求弦
的中点
的轨迹方程;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd83f319fc5f78f83d93751ef4edcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467635443c8172cc396ac3b916feb34f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d400642dfea9cf7eb05b26d62d9c73ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50da60823b387df26f73e7c2bad6fcdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c4f3fc9c421ef80dd60658fe14ef73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/21/a745d57c-7346-4f2f-983d-c82aee968e6d.png?resizew=251)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6be8b3e7ac6a923e3c36aca410bb293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09757d013574cf058d5bb944fdf034a.png)
(2)如图, 作斜率为正数的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acfc9319b4dfcefd8f0bb0338f7cbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb6101e45f8d7013bc3dc4197188c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c72229b08c676c08a3c7258895375f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
3 . 已知椭圆
上有两点
及
,直线
与椭圆交于A、B两点,与线段
交于点C(异于P、Q).
(1)当
且
时,求直线
的方程;
(2)当
时,求四边形
面积的取值范围;
(3)记直线
、
、
、
的斜率依次为
、
、
、
,当
且线段
的中点M在直线
上时,计算
的值,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c03c6b8d7418edf20f474389971352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3178e2296170fb2ba5ed2c016a1edc80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626cec0aec0243e6bbdcf264396a700e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24e616b5a35ff372c78c1472f156ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b5cc821ddbdf58518685593d614290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7571e2f20e482a852a5d4639480f6a5.png)
(3)记直线
![](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/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3307e11f7e6896e32aa510bbed949ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03b011f69dfc5262a3d82f64676739b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98e5f03e2e6d8e82c652520447dee93.png)
您最近一年使用:0次
2022-02-23更新
|
274次组卷
|
2卷引用:上海市川沙中学2022届高三下学期期中数学试题
4 . 已知椭圆
,
,
为左、右焦点,直线
过
交椭圆于
,
两点.
(1)若直线
垂直于
轴,求
;
(2)当
时,
在
轴上方时,求
、
的坐标;
(3)若直线
交
轴于
,直线
交
轴于
,是否存在直线
,使得
,若存在,求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c763113a1fc48e8acc83787b8cd24eec.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)若直线
![](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/aaff41080fdea43eea7efedf9ebc1498.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd54b527d14c877bed6de7ef490390c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6481bdb14db168814440057c358b47b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-10-16更新
|
812次组卷
|
12卷引用:上海市南汇中学2022届高三下学期期中数学试题
上海市南汇中学2022届高三下学期期中数学试题(已下线)专题17 圆锥曲线常考题型05——圆锥曲线中的存在性问题与面积问题-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)浙江省杭州市第十四中学2022-2023学年高二下学期阶段性测试(期中)数学试题(已下线)【2023】【高二下】【期中考】【368】【高中数学】【马定超收集】上海市闵行(文绮)中学2023-2024学年高三下学期3月月考数学试卷上海市闵行(文绮)中学2023-2024学年高三下学期5月月考数学试卷重庆市杨家坪中学2019-2020学年高二上学期第二次月考数学试题(已下线)专题31 圆锥曲线存在性问题的五种类型大题100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)(已下线)第13讲 椭圆-3(已下线)第28题 通性通法为根基,设参变换有妙招(优质好题一题多解)(已下线)专题24 解析几何解答题(文科)-1(已下线)专题24 解析几何解答题(理科)-1
名校
解题方法
5 . 设常数
且
,椭圆
:
,点
是
上的动点.
(1)若点
的坐标为
,求
的焦点坐标;
(2)设
,若定点
的坐标为
,求
的最大值与最小值;
(3)设
,若
上的另一动点
满足
(
为坐标原点),求证:
到直线PQ的距离是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e7930731eddbcfac592b808e9b698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35876366f005b3078d9e66ea7eab65d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d063ec7f9dbeba72fabf4437f9400e07.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8493a0cd10d3d0399173c04163740a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
2021-12-23更新
|
924次组卷
|
6卷引用:上海市崇明中学2021-2022学年高二下学期期中数学试题
上海市崇明中学2021-2022学年高二下学期期中数学试题上海市嘉定区第二中学2022-2023学年高二上学期期中数学试题上海市黄浦区2022届高三一模数学试题(已下线)上海市黄浦区2022届高三上学期一模数学试题(已下线)专题10.3—圆锥曲线—椭圆大题(定值问题)—2022届高三数学一轮复习精讲精练(已下线)押全国卷(理科)第20题 圆锥曲线-备战2022年高考数学(理)临考题号押题(全国卷)
名校
解题方法
6 . 已知椭圆
,其长轴长为短轴长的
倍,且两焦点距离为2,点
.
(1)求椭圆的方程;
(2)过点P的直线交椭圆
于M、N两点,O为坐标原点,求
面积的最大值,并求此时直线的方程;
(3)已知斜率为k的直线l交椭圆
于A、B两点,直线
、
分别交椭圆于C、D,且直线
过点
,求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a74e28144cbed9111d17dd239136f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328aaba77106396d4ca644c8b7a352e0.png)
(1)求椭圆的方程;
(2)过点P的直线交椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066ea7c8dac31105aadedad5f34d93fa.png)
(3)已知斜率为k的直线l交椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d93614e46266daac998cd98bfd95bfbc.png)
您最近一年使用:0次
7 . 已知直线l:
与椭圆C:
交于A、B两点(如图所示),且
在直线l的上方.
![](https://img.xkw.com/dksih/QBM/2021/11/12/2849537702043648/2851655053598720/STEM/f1b26880-b7d2-441c-a649-f2096567e0c3.png?resizew=280)
(1)求常数t的取值范围;
(2)若直线PA、PB的斜率分别为k1、k2,求k1+k2的值;
(3)若△APB的面积最大,求∠APB的大小,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eba60998227538aad8dd870f95c0087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7450d0b0af662741a8c76693871cfd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f847bd245d593277bd4887ff2f1e8a3a.png)
![](https://img.xkw.com/dksih/QBM/2021/11/12/2849537702043648/2851655053598720/STEM/f1b26880-b7d2-441c-a649-f2096567e0c3.png?resizew=280)
(1)求常数t的取值范围;
(2)若直线PA、PB的斜率分别为k1、k2,求k1+k2的值;
(3)若△APB的面积最大,求∠APB的大小,
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解题方法
8 . 椭圆
:
的焦点
,
是等轴双曲线
:
的顶点,若椭圆
与双曲线
的一个交点是P,
的周长为
.
(1)求椭圆
的标准方程;
(2)点M是双曲线
上任意不同于其顶点的动点,设直线
、
的斜率分别为
,
,求证
,
的乘积为定值;
(3)过点
任作一动直线l交椭圆
与A,B两点,记
,若在直线AB上取一点R,使得
,试判断当直线l运动是,点R是否在某一定直线上运动?若是,求出该直线的方程;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bf5b6dc0c77f6415940756380933f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1734bef717187708351c1be3bd035071.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)点M是双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183b6a0cef4256c9696a5bca31053da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c397129dacf0871ab2db37e60560f4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e011e14df352fcd5dad60eaf71efb4b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffd2ff2036eddcdee3aa1c14f7a7e77.png)
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解题方法
9 . 如图,过椭圆的左右焦点
分别作长轴的垂线
交椭圆于
,将
两侧的椭圆弧删除再分别以
为圆心,线段
的长度为半径作半圆,这样得到的图形称为“椭圆帽”.夹在
之间的部分称为椭圆帽的椭圆段,夹在
两侧的部分称为“椭圆帽”的圆弧段已知左右两个圆弧段所在的圆方程分别为
.
(2)已知直线l过点
与“椭圆帽”的交于两点为M,N,若
,求直线l的方程;
(3)已知P为“椭圆帽”的左侧圆弧段上的一点,直线l经过点
,与“椭圆帽”交于两点为M,N,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9ff1a2750cb58a14aba9ff3e755180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0379297ea616e33363f733e8cc447d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9f1a21521e8e894d0ca9b7ea6594d3.png)
(2)已知直线l过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f3701487f70df966b82d44bad9827a.png)
(3)已知P为“椭圆帽”的左侧圆弧段上的一点,直线l经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b1302fd5e6e4a0c7c9fab9a0f40135.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3dfef1b5b07e30ee36531e996220df.png)
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2021-10-18更新
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1302次组卷
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4卷引用:上海市上海外国语大学附属大境中学2023-2024学年高二下学期期中考试数学试卷
上海市上海外国语大学附属大境中学2023-2024学年高二下学期期中考试数学试卷上海外国语大学附属浦东外国语学校2022届高三上学期10月月考数学试题(已下线)专题02圆锥曲线全章复习攻略--高二期末考点大串讲(沪教版2020选修一)(已下线)专题16 圆锥曲线焦点弦 微点5 圆锥曲线焦点弦问题综合训练
解题方法
10 . 设直线与椭圆的方程分别为
与
,问
为何值时,
(1)直线与椭圆有一个公共点;
(2)直线与椭圆有两个公共点;
(3)直线与椭圆无公共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebb3b7f47e0decd48e64cb32aaa5903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3cb6fbb5f505fb1d08088521c17200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)直线与椭圆有一个公共点;
(2)直线与椭圆有两个公共点;
(3)直线与椭圆无公共点.
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