1 . 已知椭圆
的方程为
,斜率为
的直线
与椭圆
交于
,
两点,点
在直线
的左上方.
(1)若以
为直径的圆恰好经过椭圆右焦点
,求此时直线
的方程;
(2)求证:
的内切圆的圆心在定直线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)若以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
您最近一年使用:0次
2 . 已知P是圆C:
上的动点,点
,线段
的垂直平分线交
于点Q.
(1)求Q的轨迹
的方程;
(2)点E在x轴上,过点C的直线l交
于B,D两点,直线
,
分别交y轴于M,N两点,且
,求E的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afc954e87bd737ec051d5c94837c8a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
(1)求Q的轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)点E在x轴上,过点C的直线l交
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21ce7a35adb62932f10a65cb0a70e77.png)
您最近一年使用:0次
2020-03-15更新
|
205次组卷
|
2卷引用:安徽省六安市霍邱县第一中学2019-2020学年高二下学期开学考试文科数学试题
名校
解题方法
3 . 已知椭圆C:
(
)的两焦点与短轴两端点围成面积为12的正方形.
(1)求椭圆C的标准方程;
(2)我们称圆心在椭圆上运动,半径为
的圆是椭圆的“卫星圆”.过原点O作椭圆C的“卫星圆”的两条切线,分别交椭圆C于A、B两点,若直线
、
的斜率为
、
,当
时,求此时“卫星圆”的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
(1)求椭圆C的标准方程;
(2)我们称圆心在椭圆上运动,半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc8b26fb79c1f4d36130c41b18c0f9c.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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53232bf832d02c32acd9983ba974a98b.png)
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2020-02-27更新
|
710次组卷
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5卷引用:安徽省合肥市一六八中学2019-2020学年高三下学期第三次教学质量理科数学试题
4 . 若直线
与抛物线
交于
两个不同的点,抛物线的焦点为
,且
成等差数列,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d8041c797b98b834c70dbf7d1d4346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.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/3165071b658b916476f06efc36fdd165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-01-14更新
|
410次组卷
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4卷引用:安徽省合肥市庐阳区合肥六中、合肥八中、阜阳一中、淮北一中四校2019-2020学年高二上学期期末数学(理)试题
名校
5 . 已知椭圆
:
的左、右焦点为
,
,点
在椭圆
上,且
面积的最大值为
,周长为6.
(1)求椭圆
的方程,并求椭圆
的离心率;
(2)已知直线
:
与椭圆
交于不同的两点
,若在
轴上存在点
,使得
与
中点的连线与直线
垂直,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9df1061c3ba5151ba2f7359acaf356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53cd24fdb222c2e68c05c21600383df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/8649ce18c628d0e03e72cef541f8284f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2019-10-21更新
|
1294次组卷
|
3卷引用:安徽省宿州市泗县第一中学2018-2019学年高二下学期期末数学(文)试题
6 . 已知椭圆
,斜率为1的直线
与椭圆
交于
两点,且
.
(1)若
两点不关于原点对称,点
为线段
的中点,求直线
的斜率;
(2)若存在点
,使得
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0296bd9900adcc311f59ad44e940b86f.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/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
(2)若存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe129661004586a7720ffc98634d3b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a5142d4b4370bb2f9900136d216fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
真题
名校
7 . 已知椭圆的中心为原点
,长轴在
轴上,上顶点为
,左、右焦点分别为
,线段
的中点分别为
,且△
是面积为4的直角三角形.
(Ⅰ)求该椭圆的离心率和标准方程;
(Ⅱ)过
作直线
交椭圆于
,
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787e048d8e5402c223678e39d11b121c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1acf532db82b97a574517f5a2fae5f58.png)
(Ⅰ)求该椭圆的离心率和标准方程;
(Ⅱ)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://img.xkw.com/dksih/QBM/2012/6/20/1570893694107648/1570893699530752/STEM/f5310a42feb24650b04da06124c3d7de.png?resizew=9)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6112cb725b49eed2d7d63054e95c6.png)
![](https://img.xkw.com/dksih/QBM/2012/6/20/1570893694107648/1570893699530752/STEM/f5310a42feb24650b04da06124c3d7de.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/3/41cea6a9-2c2f-4d70-8dfd-fd2549e3eef8.png?resizew=282)
您最近一年使用:0次
2019-01-30更新
|
3721次组卷
|
17卷引用:2017届安徽屯溪一中高三上学期月考二数学(理)试卷
2017届安徽屯溪一中高三上学期月考二数学(理)试卷安徽省合肥庐阳高级中学2017-2018学年高二(上)期末考试理科数学试题安徽省六安市第一中学2017-2018学年高二上学期期末考试数学(文)试题2012年全国普通高等学校招生统一考试理科数学(重庆卷)2012年全国普通高等学校招生统一考试文科数学(重庆卷)(已下线)2013届山东省高三高考压轴理科数学试卷(已下线)2014届人教版高考数学文科二轮专题复习提分训练22练习卷2016届广东省广州实验中学高三上学期第二次段文科考数学试卷2017-2018学年高中数学(苏教版)选修1-1 阶段质量检测(二)圆锥曲线与方程2017-2018学年高中数学(苏教版)选修1-1 阶段质量检测(二) 圆锥曲线与方程浙江省余姚中学2017-2018学年高二上学期第一次质量检测试题数学黑龙江省海林市朝鲜族中学人教版高中数学选修2-1同步练习:滚动习题(二)[范围2.1~2.2](已下线)专题9.5 椭圆(讲)【文】-《2020年高考一轮复习讲练测》(已下线)卷05-备战2020年新高考数学自学检测黄金10卷-《2020年新高考政策解读与配套资源》甘肃省民乐县第一中学2020-2021学年高三上学期1月诊断考试数学(理)试题(已下线)专题9-3 圆锥曲线压轴大题五个方程框架十种题型-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)四川省遂宁市射洪中学2021-2022学年高二下学期第一次月考数学理试题
解题方法
8 . 设点
为坐标原点,椭圆
:
的右顶点为
,上顶点为
,过点
且斜率为
的直线与直线
相交于点
,且
.
(1)求椭圆
的离心率
;
(2)
是圆
:
的一条直径,若椭圆
经过
两点,求椭圆
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/5e6486784415f3537c9a13556c05d893.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/eb3a58087df44b84290f977aa5737ab9.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)
![](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/8ec416bf0140aaca8846facd72ebc198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
名校
解题方法
9 . 已知椭圆
的离心率为
, 椭圆短轴的一个端点
与两焦点
、
构成的
的面积为
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)设直线
与椭圆
交于
、
两点,线段
的垂直平分线交
轴于点
,当点T到直线l距离为
时,求直线
方程和线段AB长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb153959d3a84cc1f4846f6ffd3b015a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.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/28113019952b6f450435b9928a894751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd9f041754c54e2790f8fdf434ab148f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2018-02-06更新
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300次组卷
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2卷引用:安徽省黄山市2017-2018学年高二上学期期末考试数学(文)试题
2016高二·全国·课后作业
10 . 已知椭圆
的离心率
,焦距为2.
(1)求椭圆
的方程;
(2)已知椭圆
与直线
相交于不同的两点
,且线段
的中点不在圆
内,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe2d78f43611bad0d264eb3222f2472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2017-11-27更新
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1475次组卷
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10卷引用:安徽省芜湖市华星学校2020-2021学年高二下学期第一次月考理科数学试题
安徽省芜湖市华星学校2020-2021学年高二下学期第一次月考理科数学试题(已下线)同步君人教A版选修1-1第二章2.1.2椭圆的简单几何性质(已下线)同步君人教A版选修2-1第二章2.2.2椭圆的简单几何性质2016-2017学年河北枣强中学高二理12月月考数学试卷2016-2017学年广西桂林市桂林中学高二下学期开学考试数学(文)试卷高中数学人教版 选修2-1(理科) 第二章 圆锥曲线与方程 2.2.2 椭圆的简单几何性质高中数学人教版 选修1-1(文科) 第二章 圆锥曲线与方程 2.1.2 椭圆的简单几何性质内蒙古自治区赤峰市林西县第一中学2021-2022学年高二上学期期中数学试文科题北师大版(2019) 选修第一册 数学奇书 第二章 圆锥曲线 §4 直线与圆锥曲线的位置关系 4.1 直线与圆锥曲线的交点北师大版(2019) 选修第一册 数学奇书 学业评价(二十一) 直线与圆锥曲线的交点