名校
解题方法
1 . 已知直线
过抛物线
的焦点
,点
关于
轴的对称点为
,直线
与
轴相交于
点,则实数
的值为 ( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5b904a814c6cabc75450e899cf247e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-04-07更新
|
145次组卷
|
5卷引用:贵州省部分重点中学2019届高三上学期高考教学质量评测卷(四)(期末)数学(理)试题
贵州省部分重点中学2019届高三上学期高考教学质量评测卷(四)(期末)数学(理)试题2019届全国100所名校最新高考模拟示范卷高三数学模拟测试文科数学(二)试题山西省忻州市第一中学2020-2021学年高二下学期4月月考数学(文)试题(已下线)第三章 圆锥曲线与方程单元测试-2021-2022学年高二数学同步精品课堂讲+例+测(苏教版2019选择性必修第一册)(已下线)专题45 盘点圆锥曲线中的定点问题——备战2022年高考数学二轮复习常考点专题突破
解题方法
2 . 点
是抛物线
上一点,斜率为
的直线
交抛物线
于点
,
,且
,设直线
,
的斜率分别为
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c190e3498ab082d575c24a1a66b6da0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
![](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)
A.![]() | B.![]() | C.直线![]() ![]() | D.直线![]() ![]() |
您最近一年使用:0次
2020-06-14更新
|
334次组卷
|
2卷引用:贵州省部分学校2019-2020学年高三联合考试数学理科试题
3 . 点
是直线
上的动点,过点
的直线
、
与抛物线
相切,切点分别是
、
.
(1)证明:直线
过定点;
(2)以
为直径的圆过点
,求点
的坐标及圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd24f3c4bc9f9a75d4b28630bb630d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2020-04-12更新
|
838次组卷
|
3卷引用:贵州省贵阳市第一中学2019-2020学年高三高考适应性月考卷(六)数学(文)试题
名校
解题方法
4 . 在平面直角坐标系中,已知曲线
上的动点
到点
的距离与到直线
的距离相等.
(1)求曲线
的轨迹方程;
(2)过点
分别作射线
、
交曲线
于不同的两点
、
,且
.试探究直线
是否过定点?如果是,请求出该定点;如果不是,请说明理由
![](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/50154acc6ad77c6c777fffe3a08afb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236a066876764d090523afe0ea734a21.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e584f799ea554fc5533925ead4672501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.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/89509122e62ab0f9e7fef2158f30b7b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
5 . 在平面直角坐标系中,已知曲线
上的动点
到点
的距离与到直线
的距离相等.
(1)求曲线
的轨迹方程;
(2)过点
分别作射线
、
交曲线
于不同的两点
、
,且以
为直径的圆经过点
.试探究直线
是否过定点?如果是,请求出该定点;如果不是,请说明理由.
![](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/50154acc6ad77c6c777fffe3a08afb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236a066876764d090523afe0ea734a21.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e584f799ea554fc5533925ead4672501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
6 . 已知动圆M与直线
相切,且与圆N:
外切
(1)求动圆圆心M的轨迹C的方程;
(2)点O为坐标原点,过曲线C外且不在y轴上的点P作曲线C的两条切线,切点分别记为A,B,当直线
与
的斜率之积为
时,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa9dd4d452ba05247ea59caf9ad9fa6.png)
(1)求动圆圆心M的轨迹C的方程;
(2)点O为坐标原点,过曲线C外且不在y轴上的点P作曲线C的两条切线,切点分别记为A,B,当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2020-03-01更新
|
1131次组卷
|
5卷引用:2019届黑龙江省哈尔滨市第三中学校高三第三次模拟数学(理)试题
2019届黑龙江省哈尔滨市第三中学校高三第三次模拟数学(理)试题河南省鹤壁市高级中学2020届高三下学期线上第四次模拟数学(理)试题贵州省贵阳市修文县2022届高三下学期第二次模拟考数学(理)试题福建省漳州第一中学2022届高三上学期第四次阶段性考试数学试题(已下线)专题30 圆锥曲线求过定点大题100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)
7 . 过点
的直线
与抛物线
交于
,
两点,
为坐标原点,
.
(1)求
的值;
(2)若
与坐标轴不平行,且
关于
轴的对称点为
,求证:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
2019-05-09更新
|
1457次组卷
|
6卷引用:【市级联考】贵州省贵阳市2019届高三5月适应性考试(二)文科数学试题
【市级联考】贵州省贵阳市2019届高三5月适应性考试(二)文科数学试题【市级联考】贵州省贵阳市2019年高三5月适应性考试(二)理科数学试题2019届贵州省安顺市高考适应性考试(二)理科数学试题【校级联考】广东省六校2019届高三第四次联考文科数学试题安徽省淮南市2019-2020学年高二上学期期末数学(文)试题(已下线)专题02 化繁为简,轻松驾驭解析几何运算有技巧(第五篇)-2020高考数学压轴题命题区间探究与突破
名校
8 . 已知抛物线
:
.
(Ⅰ)
、
是抛物线
上不同于顶点
的两点,若以
为直径的圆经过抛物线的顶点,试证明直线
必过定点,并求出该定点的坐标;
(Ⅱ)在(Ⅰ)的条件下,抛物线在
、
处的切线相交于点
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
(Ⅰ)
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(Ⅱ)在(Ⅰ)的条件下,抛物线在
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e1441a49e782ff0ef46e776cde06a.png)
您最近一年使用:0次
名校
9 . 已知过点
的直线l与抛物线E:
交于点A,B.
若弦AB的中点为M,求直线l的方程;
设O为坐标原点,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbf3925a451f83180e14382d15fafe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294b85c50741fbeeeb3f52f012434afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87be53262d72dda5dd55d79ab20ff0b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526253844494fed86429e1390505e0db.png)
您最近一年使用:0次
2019-03-06更新
|
2029次组卷
|
8卷引用:贵州省黔南州2018-2019学年高二上学期期末考试数学(文)试题
贵州省黔南州2018-2019学年高二上学期期末考试数学(文)试题【市级联考】吉林省白山市2018-2019学年高二上学期期末联考数学(理)试题【市级联考】河南省新乡市2018-2019学年高二上学期期末考试数学(文)试题山西省临汾一中、翼城中学、曲沃中学等学校2018-2019学年高二上学期期末数学(文)试题安徽省滁州市九校2019-2020学年高二上学期期末考试数学(文)试题山西省2018-2019学年高二上学期期末联合考试数学(理)试题(已下线)江西省南昌市2019-2020学年进贤二中高二下学期第一次月考数学(理)试题吉林省四平市第一高级中学2019-2020学年高二上学期第三次月考数学(文)试题
名校
10 . 已知抛物线
:
,过其焦点
作斜率为1的直线交抛物线
于
,
两点,且线段
的中点的纵坐标为4.
(1)求抛物线
的标准方程;
(2)若不过原点
且斜率存在的直线
与抛物线
相交于
、
两点,且
.求证:直线
过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若不过原点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
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