解题方法
1 . 给出下列四个命题:
①若
,则
;
②当
时,
的最小值为4;
③已知
是等差数列
的前
项和,若
,则
;
④过抛物线
焦点
的直线交抛物线于
两点,则
.
其中正确命题的序号为___________ .
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed0d3e6741e0193addff8cf7b25019c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68265211ff8205d5c0ea1b5f7e20521.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/409d37d9465ec42be99d13cfbc0bc6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70ced225ea5590e06ece27b77ad3ac74.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a425978da20cebf8c4c63953579e7b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6745b23f90d2e3a2bad6048bc734bb08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47af0fa1a8a597e0d1336a5368f47084.png)
④过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf7b911d5ec34e3ffc72b89285592ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a415f13ef220884d1916203ed4e542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669b5240185e8caf113d2b5fb6a453ae.png)
其中正确命题的序号为
您最近一年使用:0次
21-22高二·江苏·单元测试
名校
解题方法
2 . 过抛物线C:
的准线上任意一点
作抛物线
的切线,切点为
,若在
轴上存在定点
,使得
恒成立,则点
的坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088fcdd595455906a1a7080d630611f5.png)
![](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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abdcad3b7a9bbb95bd573a6124b05226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-01-03更新
|
700次组卷
|
5卷引用:天津市滨海新区塘沽第一中学2021-2022学年高二上学期期末自测自评数学试题
天津市滨海新区塘沽第一中学2021-2022学年高二上学期期末自测自评数学试题(已下线)专题15 《圆锥曲线与方程》中的定点问题(1)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) (已下线)3.3(附加3)圆锥曲线定点与定值问题-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)模块三 专题5 圆锥曲线中的定值和定点问题(高二人教A)(已下线)重难专攻(十)圆锥曲线中的定点问题(核心考点集训)
解题方法
3 . 已知抛物线
的焦点为
,准线为
,过点
的直线与抛物线交于两点
,
.
①抛物线
焦点到准线的距离为
;
②若
,则
;
③
;
④过点
和抛物线顶点的直线交抛物线的准线为点
,则直线
平行于
抛物线的对称轴;
⑤绕点
旋转且与抛物线
有且仅有一个公共点的直线至多有2条.
以上结论中正确的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bd36d19352628cb54c214436ee3322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27bd43bc4af1e3b28d0de0cc561b879.png)
①抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd9956ece187cdcfcaac03526c609fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d2fa0ea5a59f2a097562e6f454127d.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c71ec44bd36a0a10f8aa693e8f2d38.png)
④过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
抛物线的对称轴;
⑤绕点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879a4007beef22e009248112d664f7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
以上结论中正确的序号为
您最近一年使用:0次
11-12高二下·湖北武汉·期中
名校
解题方法
4 . 已知抛物线
的焦点为F,直线l过点
.
(1)若点F到直线l的距离为
,求直线l的斜率;
(2)设A,B为抛物线上两点,且AB不与x轴垂直,若线段AB的垂直平分线恰过点M,求证:线段AB中点的横坐标为定值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363598fd39f2269952dc6ddd1201346c.png)
(1)若点F到直线l的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(2)设A,B为抛物线上两点,且AB不与x轴垂直,若线段AB的垂直平分线恰过点M,求证:线段AB中点的横坐标为定值
您最近一年使用:0次
2020-02-27更新
|
297次组卷
|
7卷引用:2015-2016学年天津市静海一中等六校高二上学期期末理科数学卷
名校
5 . 已知抛物线C:
经过点
,A,B是抛物线C上异于点O的不同的两点,其中O为原点.
(1)求抛物线C的方程,并求其焦点坐标和准线方程;
(2)若
,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642bade9e30b7a60c2b3b7d48d87d4f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219ba9eec5169a9844614fe8bcce5b0a.png)
(1)求抛物线C的方程,并求其焦点坐标和准线方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87be53262d72dda5dd55d79ab20ff0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a9354a07397b21c33820fc2590e814.png)
您最近一年使用:0次
2020-01-20更新
|
722次组卷
|
2卷引用:天津市和平区2019-2020学年高二上学期期末数学试题
名校
6 . 给出下列四个命题
①已知
为椭圆
上任意一点,
,
是椭圆的两个焦点,则
的周长是8;
②已知
是双曲线
上任意一点,
是双曲线的右焦点,则
;
③已知直线
过抛物线
的焦点
,且
与
交于
,
,
,
两点,则
;
④椭圆具有这样的光学性质:从椭圆的一个焦点出发的光线,经椭圆反射后,反射光线经过椭圆的另一个焦点,今有一个水平放置的椭圆形台球盘,点
,
是它的焦点,长轴长为
,焦距为
,若静放在点
的小球(小球的半径忽略不计)从点
沿直线出发则经椭圆壁反射后第一次回到点
时,小球经过的路程恰好是
.
其中正确命题的序号为__ (请将所有正确命题的序号都填上)
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.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/0a9df1061c3ba5151ba2f7359acaf356.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad0c75ce33673ec4c425896e8619e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebcff96145edc12b6146acbe99ed89e.png)
③已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.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/b5a54e0b4872cabdc0b07ea9380e4de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a350eb41c3b7e4face9c3299eff9d49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8e72f73db207c3040f143d837d5995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24529eadaef974ec0625f8ca40682e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf2c0716fb34f24ca1956700ee849cc.png)
④椭圆具有这样的光学性质:从椭圆的一个焦点出发的光线,经椭圆反射后,反射光线经过椭圆的另一个焦点,今有一个水平放置的椭圆形台球盘,点
![](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/878e89b6eca35e34c863e832a2c661db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dcc91c2ffb5571eaf944c34f5e8ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2a7b13d95229e2e938514739054541.png)
其中正确命题的序号为
您最近一年使用:0次
2020-01-08更新
|
340次组卷
|
2卷引用:天津市滨海新区滨海新区汉沽第一中学2019-2020学年高二上学期期末数学试题
名校
7 . 已知抛物线
,过原点作两条互相垂直的直线分别交
于
两点(
均不与坐标原点重合),则抛物线的焦点
到直线
距离的最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-03-29更新
|
630次组卷
|
4卷引用:天津市经济技术开发区第一中学2020-2021学年高二上学期12月月考数学试题