名校
1 . 在平面直角坐标系中,某菱形的一组对边所在的直线方程为:
,另一组对边
.则下列命题正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918a3d19a84cf5689dc1b0d01b19f618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095101a2f656d85ba4a96d06f4f16ca6.png)
A.![]() |
B.与![]() ![]() |
C.该菱形一定有内切圆和外接圆 |
D.若直线![]() ![]() ![]() |
您最近一年使用:0次
2024-02-18更新
|
73次组卷
|
2卷引用:山东省菏泽市2023-2024学年高二上学期期末教学质量检测数学试题
2 . 已知椭圆
的长轴长为4,离心率为
,则该椭圆的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-02-18更新
|
912次组卷
|
2卷引用:山东省菏泽市2023-2024学年高二上学期期末教学质量检测数学试题
解题方法
3 . 如图,已知抛物线
的焦点为F,点M在其准线上,
,直线MF的倾斜角为
,且与C交于A,B两点,O为坐标原点
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ad13028c-3880-4cd3-af11-2bb3e47f0439.png?resizew=148)
(1)求C的方程;
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411a9ad06f9fa85a4f0f178a638522a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7082b77ab14f32db29b17f95b5e2d41b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0244675766f73552e4712660cf4cb7f3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ad13028c-3880-4cd3-af11-2bb3e47f0439.png?resizew=148)
(1)求C的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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解题方法
4 . 月光石是由两种长石混合组成的具有月光效应的长石族矿物.它的截面可近似看成由半圆和半椭圆组成,如图所示,在平面直角坐标系xOy中,半圆的圆心在坐标原点,半圆所在的圆过椭圆的上焦点
,半椭圆的短轴与半圆的直径重合.若直线
与半圆交于点A,与半椭圆交于点B,则
的面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/2d6f20d5-4c4e-471d-b7be-d2902af6f1b8.png?resizew=166)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5389b197345ddd861b9eda4dc9e1fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94188fea61c347a150744709920d96e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/2d6f20d5-4c4e-471d-b7be-d2902af6f1b8.png?resizew=166)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 如图,已知圆
,圆心是点T,点G是圆T上的动点,点H的坐标为
,线段CH的垂直平分线交线段TC于点R,记动点R的轨迹为曲线E.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/7f184f36-d38a-4a16-a68d-696afedbb746.png?resizew=152)
(1)求曲线E的方程;
(2)过点H作一条直线与曲线E相交于A,B两点,与y轴相交于点C,若
,
,试探究
是否为定值?若是,求出该定值;若不是,请说明理由;
(3)过点
作两条直线MP,MQ,分别交曲线E于P,Q两点,使得
.且
,点D为垂足,证明:存在定点F,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ebdc37c4828abb80c0f3bffb9e54e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5510fbff7fdcc083ef172d4b401c2229.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/7f184f36-d38a-4a16-a68d-696afedbb746.png?resizew=152)
(1)求曲线E的方程;
(2)过点H作一条直线与曲线E相交于A,B两点,与y轴相交于点C,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9545ecde4068ea16914263cddb3e8f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cff2d267cabb5318d29e319fe65c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b385adf402cd17bddace02fdb32030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ebcef3ed51c751de97752bbf40e87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b14463c252e686a3cd0a8c4e33c02b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0165236f973be829fd3dbabe9507243.png)
您最近一年使用:0次
解题方法
6 . 已知双曲线
,点
,
都在双曲线
上,且
的右焦点为
.
(1)求
的离心率及其渐近线方程;
(2)设点
是双曲线C右支上的任意一点,记直线
和
的斜率分别为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17584c9b8f4e48c3a8e0a7c8ac626d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d338e7357317123f80aa897ab214d8.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/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15842bf8d01999770a53f70f1fca36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42623f14667ebfa914eb12d026023d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2b67088871026e040619c8f00c616c.png)
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解题方法
7 . 已知椭圆
,一组平行直线的斜率是
.
(1)当它们与椭圆相交时,证明这些直线被椭圆截得的线段的中点在同一条直线上;
(2)这组直线中经过椭圆上焦点的直线与椭圆交于
两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64b7ab668d61bcb8ec6d195c672a81e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(1)当它们与椭圆相交时,证明这些直线被椭圆截得的线段的中点在同一条直线上;
(2)这组直线中经过椭圆上焦点的直线与椭圆交于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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8 . 已知抛物线
的焦点为
,点
在抛物线上,且
,过点
作
轴于点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65e537d8264dd22ab2e2ce7dcfc6a94c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab3bbeeae1973ece0a8224d7f22bc6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2784a52c4da98dc9df661fc152fc29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.![]() | B.抛物线的准线为直线![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
解题方法
9 . 在平面直角坐标系.xOy中,设
,
两点的坐标分别为
,
.直线
,
相交于点M,且它们的斜率之积是
.
(1)求动点M的轨迹方程;
(2)记动点M的轨迹为曲线E,过
作两条互相垂直的直线
,
,
与曲线E交于A、B两点,
与曲线E交于C、D两点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc8350b12974ffc8d06fce36d158f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c2cc110e46ae4b3432814810e28bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)求动点M的轨迹方程;
(2)记动点M的轨迹为曲线E,过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f449cadb49859b80c31ef1f68bfe81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b3dff6522c24a955ea87891d2a7b25.png)
您最近一年使用:0次
2024-02-17更新
|
273次组卷
|
2卷引用:山东省济南市2023-2024学年高二上学期1月期末质量检测数学试题
解题方法
10 . 已知抛物线
的焦点为F,过点F作与x轴不垂直的直线l交C于点A,B,过点A作垂直于x轴的直线交C于点D,若点M是
的外心,则
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae0a11e98f07a03035865542297a72f.png)
您最近一年使用:0次