1 . 已知椭圆
:
经过
,
两点,M,N是椭圆
上异于T的两动点,且
,直线AM,AN的斜率均存在.并分别记为
,
.
(1)求证:
为常数;
(2)证明直线MN过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c5ad47223dcd7afbd03a26c7f6bb37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032a2eb83561061db7c31d35a93a328f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
(2)证明直线MN过定点.
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2023-03-30更新
|
925次组卷
|
6卷引用:四川省自贡市2023届高三下学期第二次诊断性考试数学(文)试题
名校
解题方法
2 . 已知椭圆
的离心率为
,设
是C上的动点,以M为圆心作一个半径
的圆,过原点作该圆的两切线分别与椭圆C交于点P、Q,若存在圆M与两坐标轴都相切.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/ae0ddc2f-2c19-4cc2-a1fa-ceb098ce66ef.png?resizew=175)
(1)求椭圆C的方程;
(2)若直线OP,OQ的斜率都存在且分别为
,
,求证:
为定值;
(3)证明:
为定值?并求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8176754726d2194c890e80df1a1f1c3a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/ae0ddc2f-2c19-4cc2-a1fa-ceb098ce66ef.png?resizew=175)
(1)求椭圆C的方程;
(2)若直线OP,OQ的斜率都存在且分别为
![](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/b4757181824e15e0f21e5bdd55448783.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f6c5fd93aed88bec58002a20ea2e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bab77b1212086d7b16e288f73a09560.png)
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2022-12-03更新
|
591次组卷
|
3卷引用:四川省成都市树德中学2022-2023学年高二上学期期中考试数学(文)试题
解题方法
3 . 已知椭圆
的焦距为2,经过点
.
(1)求椭圆
的标准方程.
(2)椭圆
的左顶点为
,过其右焦点
且斜率不为0的直线
交椭圆
于
两点,记直线
的斜率分别为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe8530b8e246a9a5ec9fe3b9c347d5a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)椭圆
![](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/a0ed1ec316bc54c37c4286c208f55667.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
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名校
解题方法
4 . 已知椭圆
经过点
.
(1)求
的标准方程;
(2)过点
的直线
交
于
两点(点
在点
的上方),
的上、下顶点分别为
,直线
与直线
交于点
,证明:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808eb66c81c7caa7df8cd77fb2c9a6b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508818c7d508fd01e85ff618c0194b70.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d8923a8755672d72ac0f3495155872.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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2024-01-16更新
|
303次组卷
|
5卷引用:四川省南充市嘉陵第一中学2023-2024学年高二下学期第三次月考(5月)数学试题
四川省南充市嘉陵第一中学2023-2024学年高二下学期第三次月考(5月)数学试题江苏省连云港市2023-2024学年高三上学期期中数学试题宁夏回族自治区2023-2024学年高二上学期期末测试数学训练卷(二)(范围:选择性必修第一册 第三章+选择性必修第二册 第四章)河北省部分高中2024届高三上学期期末数学试题(已下线)第08讲:圆锥曲线(大题) (必刷7大考题+7大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)
5 . 已知椭圆
的左、右焦点分别为
,离心率为
,且经过点
.
(1)求椭圆
的标准方程;
(2)点
是椭圆
上不在
轴上的任意一点,射线
分别与椭圆
交于点
.设
的面积分别为
.求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d82387e48eafb286785a21a8d4150f.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/32999438ca3cafa7a01040b6e99cae44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685da152c14c752f7fe4e4333d1ec4dd.png)
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2024-05-09更新
|
674次组卷
|
2卷引用:四川省百师联盟2024届高三冲刺卷(二)全国卷理科数学试题
6 . 设
、
分别是椭圆
的左、右焦点,若_____,
请在以下两个条件中任选一个补充在横线上并作答.
①四点
、
、
、
中,恰有三点在椭圆
上;
②椭圆
经过点
,
与
轴垂直,且
.
(注:如果选择多个条件分别解答,则按第一个解答计分).
(1)求椭圆
的离心率;
(2)设
是椭圆
的上顶点,过
任作两条互相垂直的直线分别交椭圆
于
、
两点,过点
作线段
的垂线,垂足为
,判断在
轴上是否存在定点
,使得
的长度为定值?并证明你的结论.
![](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/851a5d6ec23256f9b4a9e98aa92945fe.png)
请在以下两个条件中任选一个补充在横线上并作答.
①四点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f05b989842734d1afd9429d15f5484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ccebafcbec8ab901145708edf2b3da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdd68297be3e412c68d27457a9f8224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9085f45a27c7122adddfec645b233e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
②椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e97a3b321e8f5a5cc526b2b8daa702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183b6a0cef4256c9696a5bca31053da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3c9cedff7811b2f9e565bdf42bfee1.png)
(注:如果选择多个条件分别解答,则按第一个解答计分).
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/c5db41a1f31d6baee7c69990811edb9f.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a81443594dd303ef713b62378dd5c20.png)
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名校
解题方法
7 . 已知
,
分别是椭圆
:
的左,右顶点,
为椭圆
上的点,直线
,
的斜率之积为
.
(1)求椭圆
的方程;
(2)直线
与椭圆
交于
,
两点,且直线
与
相交于点
,若点
在直线
上,证明:直线
过定点.
![](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/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea8a480a2fe03293cb8303da8837d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/602baac86c2b1668ecdfadc8a5948885.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.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/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-12-14更新
|
145次组卷
|
5卷引用:四川省凉山州宁南中学2023-2024学年高二上学期期末模拟数学试题(二)
解题方法
8 . 已知椭圆T以坐标原点O为对称中心,以坐标轴为对称轴,且过
,
.
(1)求椭圆T的标准方程;
(2)若A、B为椭圆上两点,且以线段AB为直径的圆经过O点.
①求证:
为定值;
②求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f839491380e131c801e2c3c4a75bcdfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f854bbda125255ac766343c1caa71ec.png)
(1)求椭圆T的标准方程;
(2)若A、B为椭圆上两点,且以线段AB为直径的圆经过O点.
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785fc822e5e30c0a9b7fa56d7306809a.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
解题方法
9 . 在平面直角坐标系中,若点A,B是椭圆
的左,右顶点,椭圆上一点
与点A连线的斜率为
.
(1)求椭圆E的方程;
(2)经过点A的直线分别交椭圆E与直线
于P,Q两点,线段QB的中点为M,若点F的坐标为
,证明:点B关于直线FM的对称点在PF上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆E的方程;
(2)经过点A的直线分别交椭圆E与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
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10 . 已知椭圆
的左右焦点分别
,若______.
请把以下两个条件中任选一个补充在横线上作答(若都选择,则按照第一个解答给分)
①四点
中,恰有三点在椭圆C上.
②椭圆C经过
,
轴,且
.
(1)求椭圆C的方程;
(2)设点D为椭圆C的上顶点,过点D作两条互相垂直的直线分别交椭圆于A、B两点,过D作直线AB的垂线垂足为M,判断y轴上是否存在定点N,使得
为定值?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
请把以下两个条件中任选一个补充在横线上作答(若都选择,则按照第一个解答给分)
①四点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedfac2568f82d62e1afd663ca6efcd7.png)
②椭圆C经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827d2dba1eefc6237b6808e058d45f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47fb32b931ef1125d7a241d1c829e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f27b6070d21b6a3fb46e522b8b8bb2.png)
(1)求椭圆C的方程;
(2)设点D为椭圆C的上顶点,过点D作两条互相垂直的直线分别交椭圆于A、B两点,过D作直线AB的垂线垂足为M,判断y轴上是否存在定点N,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4ea7acf140086ae816a4025d2683dc.png)
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