1 . 已知椭圆
的左、右焦点分别为
,
,左顶点为
,离心率为
,经过
的直线交椭圆于
两点,
的周长为8.
(1)求椭圆
的方程;
(2)过直线
上一点P作椭圆C的两条切线,切点分别为
,
①证明:直线
过定点;
②求
的最大值.
备注:若点
在椭圆C:
上,则椭圆C在点
处的切线方程为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8376a8a3dd42eaa0558501a3e2a2bdb4.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39b4ab8209e56bf6ece460b90c3f1b9.png)
备注:若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9656735f55e5de465e5667ba578d4e.png)
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2 . 已知过圆C1:x2+y2=1上一点
的切线,交坐标轴于A、B两点,且A、B恰好分别为椭圆C2:
(a>b>0)的上顶点和右顶点.
(1)求椭圆C2的方程;
(2)已知P为椭圆的左顶点,过点P作直线PM、PN分别交椭圆于M、N两点,若直线MN过定点Q(﹣1,0),求证:PM⊥PN.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fadaabc815aa24e61d0c603f2fa754d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
(1)求椭圆C2的方程;
(2)已知P为椭圆的左顶点,过点P作直线PM、PN分别交椭圆于M、N两点,若直线MN过定点Q(﹣1,0),求证:PM⊥PN.
您最近一年使用:0次
2021-08-29更新
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11卷引用:四川省巴中市通江县通江中学2021-2022学年高二下学期3月月考数学(文科)试题
四川省巴中市通江县通江中学2021-2022学年高二下学期3月月考数学(文科)试题2020届黑龙江省哈尔滨市第三中学高三综合题(一)数学理科试题四川省广安市岳池县第一中学2019-2020学年高二6月月考数学(文)试题广东省兴宁市第一中学2021届高三上学期期末数学试题(已下线)第2章《圆锥曲线与方程》章节复习巩固(基础练)-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)(已下线)考点38 直线与圆锥曲线的位置关系-备战2022年高考数学一轮复习考点帮(浙江专用)江苏省南京市人民中学(汇文女中)2020-2021学年高二下学期期初考试数学试题四川省南充高级中学2021-2022学年高三上学期第一次月考数学(文)试题河南省濮阳市2021-2022学年高二学业质量监测理科数学试题湘鄂冀三省益阳平高学校、长沙市平高中学等七校2021-2022学年高二上学期12月联考数学试题江苏省南京市燕子矶中学2022-2023学年高二上学期期末数学试题
3 . 如图所示,椭圆
中
,椭圆离心率为
,过椭圆左焦点
作不与
轴重合的直线,与椭圆
相交于
,
两点.直线
的方程为:
,过点
作
垂线,垂足为
.
![](https://img.xkw.com/dksih/QBM/2022/4/24/2964966518300672/2967844229160960/STEM/89235358-7a23-40d2-a873-9143b184c2f4.png?resizew=297)
(1)求椭圆
的标准方程;
(2)①求证:直线
过定点,并求定点的坐标;
②求△
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5742b2684d00be50a66e01c9acb6b51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97abff83cac650930a5d9aa1cfaf594f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2022/4/24/2964966518300672/2967844229160960/STEM/89235358-7a23-40d2-a873-9143b184c2f4.png?resizew=297)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
②求△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e6508201503d042acd49341b6bc602.png)
您最近一年使用:0次
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解题方法
4 . 已知两定点
,
,动点
与两定点的斜率之积为
.
(1)求动点M的轨迹方程;
(2)设(1)中所求曲线为C,若斜率为
的直线l过点
,且与C交于P,Q两点.问:在x轴上是否存在一点T,使得对任意
且
,都有
(其中
,
分别表示
,
的面积).若存在,请求出点T的坐标;若不存在,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc269fc04b75a3b88715a30fe9c080fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d850f8e63fdf3861d2aa77cd5da2812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
(1)求动点M的轨迹方程;
(2)设(1)中所求曲线为C,若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724e11601d3807c120713018d3405d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b97b295f88972ba1c7e3cefda0885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b331262ce68c03daa803a0eedfcf4ce9.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/3adf03de34b28009480e39e8d6efc0b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32a02f53354993007080ec596fb7041.png)
您最近一年使用:0次
2022-01-28更新
|
219次组卷
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2卷引用:四川省通江中学2021-2022学年高二下学期入学考试理科数学试题