名校
解题方法
1 . 已知抛物线
:
,
为坐标原点,直线
与抛物线
交于
,
两点,且直线
,
斜率之积为
,则点
到直线
的最大距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](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)
![](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/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2 . 如图,已知直线
与抛物线
交于
两点,且
交
于点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd436ca3680ce9f9cba4b052ccdd9c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
A.若点![]() ![]() ![]() |
B.直线![]() ![]() |
C.点![]() ![]() |
D.![]() ![]() |
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2024-03-22更新
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2卷引用:广东省茂名市五校联盟2023-2024学年高二下学期3月联考数学试题
3 . 已知椭圆
:
(
)的上顶点为A,离心率为
.抛物线
:
截x轴所得的线段长为
的长半轴长.
(1)求椭圆
的方程;
(2)过原点的直线l与
相交于B,C两点,直线
分别与
相交于P,Q两点.
①证明:直线
与直线
的斜率之积为定值;
②记
和
的面积分别是
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57fec8a77d00c7ceb55311eb1f149055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)过原点的直线l与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
①证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.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/235f0a6fb218d28383e6f27f2df1f50f.png)
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4 . 如图,已知点
是焦点为
的抛物线
上一点,
,
是抛物线
上异于
的两点,且直线
,
的倾斜角互补,若直线
的斜率为
.
的斜率为定值;
(2)设焦点
到直线
的距离为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1575f952f58c4019eb75785bcd49d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6575c8e965f7c0a404fdcb4622f2be5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)设焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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2024-02-12更新
|
128次组卷
|
2卷引用:广东省茂名市高州中学2023-2024学年高二下学期5月中旬模拟数学试题
名校
解题方法
5 . 已知抛物线
经过点
,直线
与抛物线相交于不同的A、
两点.
(1)求抛物线
的方程;
(2)如果
,证明直线
过定点,并求定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73eeee75206e9fa425330f40d94e6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee808a07c981406a44a69cb124792071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-12-16更新
|
1065次组卷
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6卷引用:广东省茂名市化州市2023-2024学年高二上学期期末教学质量监测数学试题
广东省茂名市化州市2023-2024学年高二上学期期末教学质量监测数学试题新疆阿勒泰地区2023-2024学年高二上学期期末联考数学试题(已下线)【一题多解】定点最值 代数几何青海省西宁市海湖中学2023-2024学年高二下学期开学考试数学试卷福建省华安县第一中学2023-2024学年高二上学期第二次月考(12月)数学试题(已下线)第三章:圆锥曲线的方程章末综合检测卷-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)
22-23高二上·山西晋中·期末
6 . 已知抛物线
,点
是抛物线
准线上的一点,过点
作抛物线
的切线,切点分别为
,
,直线
,
的斜率分别为
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ac6188f40414f76bc754dee4a75809.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/dad2a36927223bd70f426ba06aea4b45.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/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.直线![]() ![]() | B.![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
2023-02-04更新
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7卷引用:广东省高州市2023-2024学年高二上学期期末教学质量监测数学试题
7 . 已知动圆E经过定点D(1,0),且与直线x=-1相切,设动圆圆心E的轨迹为曲线C.
(1)求曲线C的方程;
(2)设过点P(1,2)的直线l1,l2分别与曲线C交于A,B两点,直线l1,l2的斜率存在,且倾斜角互补,证明:直线AB的斜率为定值.
(1)求曲线C的方程;
(2)设过点P(1,2)的直线l1,l2分别与曲线C交于A,B两点,直线l1,l2的斜率存在,且倾斜角互补,证明:直线AB的斜率为定值.
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2020-12-07更新
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1087次组卷
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11卷引用:广东省茂名市高州中学2023-2024学年高二下学期3月滚动测试数学试题
广东省茂名市高州中学2023-2024学年高二下学期3月滚动测试数学试题(已下线)新疆部分地区2024届高三高考素养调研第二次模拟考试数学试题【全国省级联考】黑龙江省2018届高三仿真模拟(四)数学(理科)试题【全国省级联考】黑龙江省2018年普通高等学校招生全国统一考试仿真模拟(四)数学(文科)试卷安徽省阜阳市颍州区第三中学2019-2020学年高二上学期期末数学(文)试题(已下线)专题9.9 圆锥曲线的综合问题(精练)-2021年高考数学(理)一轮复习讲练测(已下线)【新教材精创】3.3.2+抛物线的简单几何性质(2)+导学案-人教A版高中数学选择性必修第一册(已下线)第九单元 解析几何(B卷 滚动提升检测)-2021年高考数学(理)一轮复习单元滚动双测卷(已下线)第九课时 课后 3.3.2 第2课时 抛物线的方程及性质的应用沪教版(2020) 选修第一册 精准辅导 第2章 2.4(2) 抛物线的性质云南省大理市大理州实验中学2021-2022学年高二下学期见面考试数学试题