1 . 动点
与定点
的距离和点
到定直线
的距离之比是常数
.记点
的轨迹为
,过点
且不与
轴重合的直线
交
于
,
两点.
(1)求点
的轨迹方程;
(2)设
的左顶点为
,直线
,
和直线
分别交于点
,
,记直线
,
的斜率分别为
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.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/acc290b44635265137fdf13146b6a6d9.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)设
![](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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360496a4f5cc8a5faca5e089ae4f9531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
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解题方法
2 . 已知曲线
与y轴交于A,B两点,P是曲线C上异于A,B的点,若直线AP,BP斜率之积等于
,则C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c623fe58727acdd1fd4964b4947df4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03aa30b6d5bfcefb197cc2046479ed65.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-02-05更新
|
440次组卷
|
3卷引用:湖北省荆州市八县市区2023-2024学年高二上学期1月期末联合考试数学试题
湖北省荆州市八县市区2023-2024学年高二上学期1月期末联合考试数学试题河南省南阳市第一中学校2023-2024学年高二下学期开学考试数学试题(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
3 . 已知点
和点
是曲线
上的两点,且点
的横坐标是
,点
的纵坐标是
,求:
(1)割线
的斜率;
(2)在点
处的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d794141572c8b1e70957754f32b9eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
(1)割线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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4 . 已知直线l与抛物线
交于A,B两点,O为坐标原点,若直线OA,OB的斜率
,
满足
,则直线l恒过定点( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a802efc6b05133a91833e2f7074586.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-16更新
|
539次组卷
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4卷引用:安徽省蚌埠市第二中学2023-2024学年高二上学期12月月巩固检测数学试题
5 . 已知直线l:
的图象与曲线C:
有且只有一个交点,则实数k的取值范围是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530943b9433ed5e507fc5ef099f3dd85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db55e6eca1e746667b6cfbc5dc304924.png)
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2023-12-22更新
|
224次组卷
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4卷引用:山东省枣庄市薛城实验中学等校2023-2024学年高二上学期12月大联考数学试题
山东省枣庄市薛城实验中学等校2023-2024学年高二上学期12月大联考数学试题(已下线)2.1.3 直线与圆的位置关系(八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)山东省临沂市多校2023-2024学年高二上学期12月大联考数学试题广东省茂名市高州中学2023-2024学年高二下学期5月第一次模拟数学试卷
解题方法
6 . 为了保护河上古桥
,规划建一座新桥
,同时建立一个圆形保护区.规划要求:新桥
与河岸
垂直,保护区的边界为圆心
在线段
上,并与
相切的圆,且古桥两端
和
到该圆上任意一点的距离均不小于
.经测量点
位于点
正北方向
处,点
位于
正东方向
处(
为河岸),
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/2279e0da-3dfa-44ab-b8fe-30d4d967be3b.png?resizew=177)
(1)求新桥
的长;
(2)当
多长时,圆形保护区面积最大.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef9bd9f3d93bc6ef900f95b3bf4a8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c758c27bec97c234d1d818c40f3d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b152350f99f27608bb82ba8931cb07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6df0766fe60149908607945a5bfbe4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/2279e0da-3dfa-44ab-b8fe-30d4d967be3b.png?resizew=177)
(1)求新桥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
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解题方法
7 . 已知椭圆
与抛物线
交于点
,直线
与
轴的交点既是
的右焦点,也是
的焦点,点
关于原点的对称点分别为
,点
是
上与
均不重合的点,记直线
的斜率分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4762ec251b2d6749024ae68f74e9a650.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0107aa23cf707446f947fa236421c1f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77993759b8615ef0b42cb56ef027ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4dfc408125cc3d651bc9123abd77ecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b5f5621f4805a499c715f4f7cc6f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d8707cafd80cde5c561e2b5a3531c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4762ec251b2d6749024ae68f74e9a650.png)
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8 . 已知过点,
的直线的倾斜角为60°,则实数
您最近一年使用:0次
2023-11-23更新
|
772次组卷
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7卷引用:山东省临沂市沂水县2023-2024学年高二上学期期中考试数学试题
山东省临沂市沂水县2023-2024学年高二上学期期中考试数学试题江西省抚州市资溪县第一中学2023-2024学年高二上学期期中调研数学试题(已下线)模块一 专题3 直线与圆 期末终极研习室(2023-2024学年第一学期)高二人教A版陕西省汉中市西乡县第一中学2023-2024学年高二上学期第二次(12月)月考数学试题四川省成都市武侯高级中学2023-2024学年高二上学期12月月考数学试题(已下线)专题02 直线和圆的方程(1)(已下线)1.1 直线的倾斜角与斜率(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
9 . 设点
、
,若直线
过点
且与线段
不相交,则直线
的斜率
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51116e96f4c35d90677e91e0aa914111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7727391bd56839d2b8d6879b8e6bf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
10 . 已知实数x、y满足方程,当
时,则
的取值范围是
您最近一年使用:0次
2023-11-15更新
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286次组卷
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3卷引用:广东省广州市六十五中2023-2024学年高二上学期期中数学试题
广东省广州市六十五中2023-2024学年高二上学期期中数学试题广东省普宁市勤建学校2023-2024学年高二上学期第二次调研数学试题(已下线)1.1 直线的倾斜角与斜率(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)