真题
解题方法
1 . 如图,椭圆
的右焦点为
,过点F的一动直线m绕点F转动,并且交椭圆于A、B两点,P为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/bec862e1-5fef-47aa-9ab3-a9c82f04ae84.png?resizew=159)
(1)求点P的轨迹H的方程;
(2)在Q的方程中,令
,
,设轨迹H的最高点和最低点分别为M和N.当
为何值时,
为一个正三角形?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011e2d4e2fc81bf00711025de8b31175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6fe0f38ab3095ac6575faa02914b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/bec862e1-5fef-47aa-9ab3-a9c82f04ae84.png?resizew=159)
(1)求点P的轨迹H的方程;
(2)在Q的方程中,令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e598f08618337323f0ca508a99c4331c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5379dd4f562e89b5375ef7de6a6a1907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a33181b27b10690b4913595f8c1f46e.png)
您最近一年使用:0次
真题
2 . 函数
是定义在
上的增函数,满足
且
,在每个区间
上,
的图象都是斜率为同一常数k的直线的一部分.
(1)求
及
的值,并归纳出
的表达式;
(2)设直线
,
,
轴及
的图象围成的梯形的面积为
,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40232336e78c17b8fad52200f71b24a2.png)
,求
的表达式,并写出其定义域和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31cc0ada3e13a381c1d4186d239ebcf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebff8ae41f28f728a759a4b990273d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54b6a060d6c51a328341df76013bd89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71202e43f6e40558126523ccc77d59f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44328a5346f0a5eea5e829cf55954c74.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c25180a82381944e33a5a3545d81b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab56c528a11096103d589b05026e7100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f766f204cf98d973ad5abe03b235e95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40232336e78c17b8fad52200f71b24a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804ab1fdb8a60edee9bbd2b787fdcac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90cb6e03196a239ac1eff7929a7eb301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3465f50ce6b7704c17846758413f00d5.png)
您最近一年使用:0次
解题方法
3 . 已知椭圆
的一个顶点为
,离心率为
,右焦点为F,其中O为原点.
(Ⅰ)求椭圆的方程;
(Ⅱ)设点C满足
,点B在椭圆上(B异于椭圆的顶点).
(ⅰ)直线
与以C为圆心的圆相切于点P,且P为线段
的中点,求实数m的取值范围;
(ⅱ)若
,点B在第四象限,且
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a12f0224fb7bf5096ed129922bf0ded3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(Ⅰ)求椭圆的方程;
(Ⅱ)设点C满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2631dc0165c92a99eaf4c4d12f5a74b.png)
(ⅰ)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01976af20d1652c65938fdf0d469c669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b8765cf37a19ed0c76f5ab516ce697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
19-20高一·浙江·期末
解题方法
4 . 已知椭圆
的左、右焦点分别为
,过
的直线
不垂直坐标轴,与椭圆交于
两点,M是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/9d625140-e862-4b08-b849-4352a32e4f7d.png?resizew=171)
(1)若点M的横坐标为
,求点M的纵坐标;
(2)记
的斜率分别为
,是否存在直线
使得
成等差数列,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/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bba0bd73a215dfef56845811bc856d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/16/9d625140-e862-4b08-b849-4352a32e4f7d.png?resizew=171)
(1)若点M的横坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f43087348426ebac7552e7d0a9c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd1d510156331bf428f231ab4f7d5d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
5 . 已知椭圆
:
的一个焦点在直线
上,且该椭圆的离心率
.
(1)求椭圆
的标准方程
(2)过椭圆
的右焦点
作直线与椭圆
交于不同的两点
,
,试问在
轴上是否存在定点
使得
(
为坐标原点)?若存在求出点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce51aae55ad6738d896866f5d7eb5a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/e57610afd116ab84660c807cc1aa3819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-12-02更新
|
727次组卷
|
4卷引用:河南省豫南九校2020-2021学年上期高二第三次联考(11月)文数试卷试题
名校
6 . 设
是定义在
上的函数,且
,对任意
,
,若经过点
、
的直线与
轴的交点是
,则称
为
、
关于函数
的平均数,记为
.
(1)若
,求
的表达式;
(2)若
,求出所有满足条件的
的解析式;
(3)若对任意
,
,且
,都有
成立,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fed3c00731e2b8cb28168839363e48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb16534dcb01977caa20f738f43158a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7615495e833d173a8845b19405ba3a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c248c15da679e72278636cb731b7230a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c0668061426d6a0e63006d263c7815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c248c15da679e72278636cb731b7230a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4028849df8ded22fa2a5c2aead15a9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79657921c225d5a6a7d124ebfdf11d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af175d95e0acabd3cbd027b7192aee5d.png)
您最近一年使用:0次
名校
7 . 已知斜率存在的直线
交椭圆
:
于
,
两点,点
是弦
的中点,点
,且
,
,则直线
的斜率为( ).
![](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/6205da5e1d2730ee0b3de8bca3e29f5e.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a29ba49963134a7232fa8574105fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ad95e65f60ba5bcc08769f7f43241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36de646ede9e491319790c67ebdee80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-10-27更新
|
904次组卷
|
2卷引用:河北省张家口市邢台市衡水市2021届高三上学期摸底联考(新高考)数学试题
名校
解题方法
8 . 已知点
为抛物线
上异于原点
的动点,
为
的焦点.若
,则直线
的斜率的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a21beb3c88e85fd5891d3a98fdd9ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/1c03ef614d6099208fffdba570322ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2020-07-22更新
|
152次组卷
|
2卷引用:河南省大联考2020届高三阶段性测试(七)理科数学试题
9 . 设椭圆E:
+
=1(a>b>0)的左、右焦点分别为F1,F2,过点F1的直线交椭圆E于A,B两点.若椭圆E的离心率为
,三角形ABF2的周长为4
.
(1)求椭圆E的方程;
(2)设不经过椭圆的中心而平行于弦AB的直线交椭圆E于点C,D,设弦AB,CD的中点分别为M,N,证明:O,M,N三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7355be4fcbc3130a5951364a3be76d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5268413295580cfda0755ab458b36b64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
(1)求椭圆E的方程;
(2)设不经过椭圆的中心而平行于弦AB的直线交椭圆E于点C,D,设弦AB,CD的中点分别为M,N,证明:O,M,N三点共线.
您最近一年使用:0次
10 . 已知函数
,给出下面三个结论:
① 函数
在区间
上单调递增,在区间
上单调递减;
② 函数
没有最大值,而有最小值;
③ 函数
在区间
上不存在零点,也不存在极值点.
其中,所有正确结论的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3d74bc831a959f5d2a2b016548eba0.png)
① 函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcbc9bfba3b934d61a96ac846996f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88e93310e85e58313d4ec99a2cb0553.png)
② 函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
③ 函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083479b94380e8d659eff92d10a1989d.png)
其中,所有正确结论的序号是( )
A.①② | B.①③ | C.②③ | D.①②③ |
您最近一年使用:0次