名校
1 . 如图,
平面
为
中点,
,
,点
为平面
内动点,且
到直线
的距离为
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1183ee88499cc74960af0e3124a6eac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f2ab6093c8e91a2c89b47687e0b878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8f34f2048a0eece64a4bbbc11da7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ed13caca17a5480dda83a6a5498976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://img.xkw.com/dksih/QBM/2021/5/25/2728858708451328/2730904957575168/STEM/f119a082-2e7b-4b41-becd-70a8af611197.png)
您最近一年使用:0次
2021-05-28更新
|
1460次组卷
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6卷引用:上海市青浦高级中学2021届高三三模数学试题
上海市青浦高级中学2021届高三三模数学试题上海市青浦区2021届高三三模数学试题(已下线)考点44 曲线与方程-备战2022年高考数学(理)一轮复习考点帮(已下线)课时34 曲线和方程-2022年高考数学一轮复习小题多维练(上海专用)(已下线)专题26 求动点轨迹方程 微点2 定义法求动点的轨迹方程(已下线)第12练 空间直线、平面的垂直-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)
2 . 已知直线
交抛物线
于
两点.
(1)设直线
与
轴的交点为
,若
,求实数
的值;
(2)若点
在抛物线
上,且关于直线
对称,求证:
四点共圆:
(3)记
为抛物线
的焦点,过抛物线
上的点
作准线的垂线,垂足分别为点
,若
的面积是
的面积的两倍,求线段
中点的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c64298f6e7554ce11472f2197d45b3.png)
(1)设直线
![](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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c80fbad05116a915af3af4e8238f790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89dfcc5ea5ad1c0c8aba49ee618d72f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0836482a7ed1109ddd7308ce55b859b.png)
(3)记
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c49492d424632c63476cd61c0695958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ccac4d4eb756702c95b8648c516f50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116d9e66bd64091223a331be57aa9c8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adccd1dd14171c8c29d4a3836728c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
3 . 已知直线
与椭圆
交于
、
两点(如图所示),且
在直线
的上方.
![](https://img.xkw.com/dksih/QBM/2021/5/18/2723889934524416/2728001939791872/STEM/d597540c3de24d17bbd9f2a279e873cc.png?resizew=185)
(1)求常数
的取值范围;
(2)若直线
、
的斜率分别为
、
,求
的值;
(3)若
的面积最大,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10462edd0dbd28fc3908fe32726211a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f60eef6cf563ceb168e36025d023db5.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/5dba969413d0c05cfea8cae5b37a7c21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2021/5/18/2723889934524416/2728001939791872/STEM/d597540c3de24d17bbd9f2a279e873cc.png?resizew=185)
(1)求常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若直线
![](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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
您最近一年使用:0次
4 . 已知椭圆
=1上有两点P(﹣2,1)及Q(2,﹣1),直线l:y=kx+b与椭圆交于A、B两点,与线段PQ交于点C(异于P、Q).
(1)当k=1且
时,求直线l的方程;
(2)当k=2时,求四边形PAQB面积的取值范围;
(3)记直线PA、PB、QA、QB的斜率依次为k1、k2、k3、k4.当b≠0且线段AB的中点M在直线y=﹣x上时,计算k1⋅k2的值,并证明:k12+k22>2k3k4.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c03c6b8d7418edf20f474389971352.png)
(1)当k=1且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72313ccba4d3c4329372e40f0d076bff.png)
(2)当k=2时,求四边形PAQB面积的取值范围;
(3)记直线PA、PB、QA、QB的斜率依次为k1、k2、k3、k4.当b≠0且线段AB的中点M在直线y=﹣x上时,计算k1⋅k2的值,并证明:k12+k22>2k3k4.
您最近一年使用:0次
5 . 已知抛物线
的焦点为
,直线
交抛物线于不同的
两点.
(1)若直线
的方程为
,求线段
的长;
(2)若直线
经过点
,点
关于
轴的对称点为
,求证:
三点共线;
(3)若直线
经过点
,抛物线上是否存在定点
,使得以线段
为直径的圆恒过点
?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/745de5ef1fd897d16e37464172d5e8c9.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)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cc0f9aa168e43cc5759f017d69b498.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/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc974093c70ddb5acdbae59378bed42.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd99db7870f44cc39d36e7a7b9beb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2021-05-11更新
|
1031次组卷
|
5卷引用:上海市松江区2021届高三二模数学试题
上海市松江区2021届高三二模数学试题(已下线)考向25 直线与方程-备战2022年高考数学一轮复习考点微专题(上海专用)上海市控江中学2022届高三下学期3月月考数学试题上海市格致中学2023届高三下学期3月阶段性测试数学试题上海市浦东新区建平中学2024届高三下学期2月考试数学试卷
6 . 曲线
与曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fb8742324ca04e5c5f9a2e92e240e9.png)
在第一象限的交点为
.曲线
是
(
)和
(
)组成的封闭图形.曲线
与
轴的左交点为
、右交点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/c62720f8-b060-4076-8cd6-90cba74a716d.png?resizew=241)
(1)设曲线
与曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fb8742324ca04e5c5f9a2e92e240e9.png)
具有相同的一个焦点
,求线段
的方程;
(2)在(1)的条件下,曲线
上存在多少个点
,使得
,请说明理由.
(3)设过原点
的直线
与以![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928d1325e0f48501a6e1680b814eb0f7.png)
为圆心的圆相切,其中圆的半径小于1,切点为
.直线
与曲线
在第一象限的两个交点为
.
.当
对任意直线
恒成立,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7261298d9edd1d9a75eb9aeb1e686ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fb8742324ca04e5c5f9a2e92e240e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9cd3690e7aa3debb1ed054a9f622da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7261298d9edd1d9a75eb9aeb1e686ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a254a2539e3fddd2ed1e11fe17ef48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fb8742324ca04e5c5f9a2e92e240e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dee41282d614039c13dcdc6d71f65e7.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/c62720f8-b060-4076-8cd6-90cba74a716d.png?resizew=241)
(1)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7261298d9edd1d9a75eb9aeb1e686ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fb8742324ca04e5c5f9a2e92e240e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9cd3690e7aa3debb1ed054a9f622da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
(2)在(1)的条件下,曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc916165b2d9891d60c235da991182d6.png)
(3)设过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/928d1325e0f48501a6e1680b814eb0f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cea72e0c37257bcfd85a59ef8dd0f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc37ebff7b12c6b1a6aedb68206a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2021-05-11更新
|
804次组卷
|
4卷引用:上海市奉贤区2021届高三二模数学试题
上海市奉贤区2021届高三二模数学试题(已下线)上海市华东师范大学第二附属中学2021-2022学年高二上学期期末数学试题上海市南洋模范中学2021-2022学年高二下学期期中数学试题(已下线)期中模拟预测卷02(测试范围:选修一全部内容)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)
7 . 如图,已知椭圆
的左右顶点分别为A、B,P是椭圆
上异于A、B的一点,直线
,直线
、
分别交直线l于两点C、D,线段
的中点为E.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712323799859200/2715189758140416/STEM/1ada3aaccf274444ba0f2583744b085c.png?resizew=224)
(1)设直线
、
的斜率分别为
、
,求
的值;
(2)设
、
的面积分别为
、
,如果
,求直线
的方程;
(3)在x轴上是否存在定点
,使得当直线
、
的斜率
、
存在时,
为定值?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7b1b8a84ae7a1b2243b78cc932860d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712323799859200/2715189758140416/STEM/1ada3aaccf274444ba0f2583744b085c.png?resizew=224)
(1)设直线
![](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/b8f145b2ee281664660dea890bb24e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0d3de89a3c9fb5f775b2dab1842ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29f704ed1e1faa4ad7cd45c34cfb7a6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acefc1a2f02c6fcf971b8038323ea03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
(3)在x轴上是否存在定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432aae51854129e8c10f7c34c0c3a79f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d8e33929752b1cb4dd36ee9b98b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94803c9730f71fae718a49d175764626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a5f6ebeb8236a8076063bdd38c7b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb2a5a3cf8b042db94b784a6b1e2556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb2a5a3cf8b042db94b784a6b1e2556.png)
您最近一年使用:0次
2021-05-06更新
|
252次组卷
|
2卷引用:上海市闵行区2021届高三二模数学试题
解题方法
8 . 已知
、
分别是椭圆
的左右顶点,
为坐标原点,
,点
在椭圆
上.过点
的直线
交椭圆
于
、
两个不同的点.
(1)求椭圆
的标准方程;
(2)若点
落在以线段
为直径的圆的外部,求直线
的倾斜角
的取值范围;
(3)当直线
的倾斜角
为锐角时,设直线
、
分别交
轴于点
、
,记
,
,求
的取值范围.
![](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/91665878e65daa8b9267819d5310fd0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0907a673d52825cd7df84b400972d4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500272f9f312e2bc0f32e4afc058db41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bab45799f9f8d0374f529e8b30a0b27.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)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cfc9b28711b4e9c4b554202fe46fe6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bd0693e932eb65b222f3453e04280b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
名校
解题方法
9 . 已知椭圆
:
的左右焦点分别为
,过点
的直线
交椭圆
于不同的两点
.
(1)若直线
经过
,求
的周长;
(2)若以线段
为直径的圆过点
,求直线
的方程;
(3)若
,求实数
的取值范围.
![](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/32366143230ca122894a4bada7c7b96d.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/f6bce3d91ca23b86d8c6625f2632e437.png)
(1)若直线
![](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/35eb8a895a6122917c531afea1a83284.png)
(2)若以线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/792696ebeadfbec66792c0f07870aa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2021-05-05更新
|
2432次组卷
|
7卷引用:上海市浦东新区2021届高三二模数学试题
上海市浦东新区2021届高三二模数学试题上海市实验学校2023届高三下学期开学考试数学试题上海市曹杨中学2023-2024学年高三上学期期中考试数学试卷(已下线)专题12 定比点差法及其应用 微点3 定比点差法综合应用(二)——解决范围、最值、探索型以及存在性问题(已下线)专题33 圆锥曲线中的向量问题-1上海市川沙中学2022-2023学年高二下学期3月月考数学试题(已下线)重难点突破10 圆锥曲线中的向量问题(五大题型)
解题方法
10 . 椭圆
的右顶点为
,焦距为
,左、右焦点分别为
、
,
为椭圆
上的任一点.
(1)试写出向量
、
的坐标(用含
、
、
的字母表示;
(2)若
的最大值为
,最小值为
,求实数
、
的值;
(3)在满足(2)的条件下,若直线
与椭圆
交于
、
两点(
、
与椭圆的左右顶点不重合),且以线段
为直径的圆经过点
,求证:直线
必经过定点,并求出定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c240561788bc63f41a6703219fb66d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91495cadae88e26c662dac9f5e8e24b8.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/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)试写出向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af48b76e202b995ac17bb1861f71252b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fcd7dffad591ca6124da0e58ee91f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112f9185c7d48b015d9cd0525616b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddc29037a26719130e6548f25a2500a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)在满足(2)的条件下,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次