名校
解题方法
1 . 已知椭圆
过点
,且离心率为
.设
,
为椭圆
的左、右顶点,
为椭圆上异于
,
的一点,直线
,
分别与直线
相交于
,
两点,且直线
与椭圆
交于另一点
.
(1)求椭圆
的标准方程;
(2)求证:直线
与
的斜率之积为定值;
(3)判断三点
,
,
是否共线:并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f780f4f03699023b1322a1e002539.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/c5db41a1f31d6baee7c69990811edb9f.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.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/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
(3)判断三点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2022-10-11更新
|
1674次组卷
|
9卷引用:江苏省金陵中学集团南京市人民中学2021-2022学年高二上学期10月月考数学试题
2 . 如图,已知椭圆
,矩形ABCD的顶点A,B在x轴上,C,D在椭圆
上,点D在第一象限.CB的延长线交椭圆
于点E,直线AE与椭圆
、y轴分别交于点F、G,直线CG交椭圆
于点H,DA的延长线交FH于点M.
![](https://img.xkw.com/dksih/QBM/2021/1/13/2635062232326144/2636119953145856/STEM/0d304ada-7221-4566-ab41-d75b8ee9bbdb.png)
(1)设直线AE、CG的斜率分别为
、
,求证:
为定值;
(2)求直线FH的斜率k的最小值;
(3)证明:动点M在一个定曲线上运动.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d366fe265032467147cc806f240e6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://img.xkw.com/dksih/QBM/2021/1/13/2635062232326144/2636119953145856/STEM/0d304ada-7221-4566-ab41-d75b8ee9bbdb.png)
(1)设直线AE、CG的斜率分别为
![](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/67351fe10fcfc3f9072eec4c60bfaaa5.png)
(2)求直线FH的斜率k的最小值;
(3)证明:动点M在一个定曲线上运动.
您最近一年使用:0次
2021-01-14更新
|
3306次组卷
|
10卷引用:江苏省泰州市2020-2021学年高三上学期期末数学试题
江苏省泰州市2020-2021学年高三上学期期末数学试题江苏省扬州中学2020-2021学年高二下学期开学考试数学试题(已下线)黄金卷08-【赢在高考·黄金20卷】备战2021年高考数学全真模拟卷(江苏专用)(已下线)第3章 圆锥曲线与方程(培优卷)-2021-2022学年高二数学新教材单元双测卷(苏教版2019选择性必修第一册)(已下线)专题26 椭圆(解答题)-2021年高考数学(理)二轮复习热点题型精选精练(已下线)专题25 椭圆(解答题)-2021年高考数学二轮复习热点题型精选精练(新高考地区专用)(已下线)仿真系列卷(05) - 决胜2021高考数学仿真系列卷(江苏等八省新高考地区专用)(已下线)3.1椭圆C卷(已下线)专题7 圆锥曲线之极点与极线 微点1 圆锥曲线之极点与极线(已下线)第五篇 向量与几何 专题4 极点与极线 微点1 圆锥曲线之极点与极线(一)
3 . 已知椭圆
的左、右焦点分别为
.等轴双曲线
的顶点是
的焦点,焦点是
的顶点.点
在
上,且位于第一象限,直线
与
的交点分别为
和
,其中
在
轴上方.
(1)求
和
的方程;
(2)求证:
为定值;
(3)设点
满足直线
的斜率为1,记
的面积分别为
.从下面两个条件中选一个,求
的取值范围.
①
;②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38e81c217824885baa1a5a440a8091b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d82387e48eafb286785a21a8d4150f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c888eba416ceca9d0b82e8cae3017846.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b406c5e06b7790b2e481a8ce3f5e33c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8a75b5ec2fb0f16fc29969aa624849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6229cf67fdcbee978762d4e3dabd05dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c083616512712466bf5a652913c9828d.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
经过
和
,
分别为椭圆的左顶点、右顶点、上顶点.
(1)求椭圆
的标准方程;
(2)过
轴上点
(点
在椭圆
长轴上)作直线交椭圆
两点,且
,若
,求
点的坐标;
(3)过点
作直线交椭圆
于
点,交直线
于
,直线
于
轴相交于
,求证:
为定值,并求此定值.(其中
分别为直线
和直线l,
的斜率).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1bbd2face8220cbd14191212588aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2314fc922502d8fc6d13e4b9f2775b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd07fb0b22450681d23d5f0513d8e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7af7c5df749c6fa9bbe87faa72c66d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94e87c1ed4c9c0cd0f9e1f10f11a35f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21791b26a0b406302709f9776dd9f28f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.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/c4849d0599bbeaccc05eb0cece91ec97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eacfcd9c21fffe2820a00dd4f09ef25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
您最近一年使用:0次
名校
解题方法
5 . 在平面直角坐标系
中,已知椭圆
经过点
,直线
与
轴交于点
,过
的直线
与
交于
两点(异于
),记直线
和直线
的斜率分别为
.
(1)求
的标准方程;
(2)求
的值;
(3)设直线
和直线
的交点为
,求证:
在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c118b51ab426bc1c1b56179094f146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec30037a621b23ade12cf58e42c4059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8533b4c6574df4f59b2ecc99e5c458db.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e3016db8a12fd848e8c4b93c11070d.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2024-01-29更新
|
554次组卷
|
3卷引用:江苏省苏州市2024届高三上学期学业质量阳光指标调研数学试题
江苏省苏州市2024届高三上学期学业质量阳光指标调研数学试题山东省东营市第一中学2023-2024学年高二下学期开学收心考试数学试题(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
6 . 已知椭圆
的右焦点为
,点
在椭圆
上,且
垂直于
轴.
(1)求椭圆
的方程;
(2)直线
斜率存在,交椭圆
于
两点,
三点不共线,且直线
和直线
关于
对称.
(ⅰ)证明:直线
过定点;
(ⅱ)求
面积的最大值.
![](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/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016e82617e4586c46e55b27cd604db1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
(ⅰ)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
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2024-04-05更新
|
1404次组卷
|
2卷引用:2024届江苏省南通市徐州市高三2月大联考模拟预测数学试题
7 . 如图,已知椭圆
与椭圆
有相同的离心率,点
在椭圆
上.过点
的两条不重合直线
与椭圆
相交于
两点,与椭圆
相交于
和
四点.
的标准方程;
(2)求证:
;
(3)若
,设直线
的倾斜角分别为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40de76911377ce524655488973914c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d5915ae756cee0e30fed15da2ae16d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9b77128eab3b2c8d42f0031c9d87cc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b035d7e2a68f56d04ad9b79fab7b3b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc851d438b2124f8ca9bb48a637e8705.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca98887356d093d283abf16635db7249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
您最近一年使用:0次
2024-02-29更新
|
1189次组卷
|
4卷引用:江苏省南菁高中、常州一中2023-2024学年高二下学期3月月考数学试题
名校
解题方法
8 . 已知椭圆
的左焦点
,点
在椭圆
上,过点
的两条直线
分别与椭圆
交于另一点
,且直线
的斜率满足
.
(1)求椭圆
的方程;
(2)证明直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63587f0178ca6f60d893e2e29d231a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d059a0d71bddb677c603d84fac444b.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/790ef3382b1c731f2885eecfd92c2a86.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/b86d920459c8efe08d73807772a0efc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8b196ae90f5bb109698dd7bcfc510f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2024-05-11更新
|
1228次组卷
|
3卷引用:数学(江苏专用03)
9 . 已知椭圆
的右焦点为
,直线
与
相交于
、
两点.
(1)求直线l被圆
所截的弦长;
(2)当
时,
.
(i)求
的方程;
(ii)证明:对任意的
,
的周长为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7b07ace87ed58fdc1f1bc78a04aeda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6199fedebb50f6e78edf3c857a661fe.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/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求直线l被圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b96eda0601673fafb836643969914f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ad7d1e3fad77908415415d6b2a90f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519471c8b171671833ad6e033ac26cea.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(ii)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3744ee15af01a8e7c0f126edb5f68132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
您最近一年使用:0次
2024-02-28更新
|
902次组卷
|
4卷引用:江苏省南通市海安高级中学2024届高三下学期开学考试数学试题
名校
解题方法
10 . 已知椭圆C:
(
)的左、右焦点分别为
,
,右顶点为A,且
,离心率为
.
(1)求C的方程;
(2)已知点
,M,N是曲线C上两点(点M,N不同于点A),直线
分别交直线
于P,Q两点,若
,证明:直线
过定点.
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba7267be8fb3db5ec612fb9d8950239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求C的方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42f05b013e4b7166cbc87c5a83d6a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d42cb68c5c877a455ba7ac0a6b6a651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1c84057882768f20a01365c81b6760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab1bf37bfecae9206e09d864da4c796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2024-02-14更新
|
952次组卷
|
2卷引用:江苏省盐城市滨海县五汛中学2023-2024学年高三下学期高考适应性考试数学试题