1 . 已知抛物线
:
的焦点为
.
(1)点
、
满足
,当点
在抛物线
上运动时,求动点
的轨迹方程;
(2)在
轴上是否存在点
,使得点
关于直线
的对称点在抛物线
上?如果存在,求所有满足条件的点
的坐标;如果不存在,请说明理由.
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34dda776b1da3aaaa5ee4092e6832444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2 . 已知双曲线
:
,直线
交双曲线的左支于
、
两点.
(1)求实数
的取值范围;
(2)如果
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231896d2386c924306fce5ccf9f9e8a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4701c1af1f541cf716d3cbcf12c8187e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
3 . 设点
、
,动点
满足
,
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过定点
(
)作直线
交曲线
于
、
两点,设
为坐标原点,若直线
与
轴垂直,求
面积的最大值;
(3)过点
作直线
交曲线
于
、
两点,在
轴上是否存在一点
,使直线
和
的斜率的乘积为非零常数?若存在,求出点
的坐标和这个常数;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4a7482cb81b34df5a11807b8136a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60cfc83cab6cd17842f28b9c37836673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f595683f69d5d6b5ca76408b0ff6ff17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8885ec539bee393d1dec8c072b8174cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a21ae339bab079581b6d5b1198da0730.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
名校
4 . 如图,在平面直角坐标系
中,
、
分别是椭圆
的顶点.过坐标原点的直线交椭圆于
、
两点,其中
在第一象限.过点
作
轴的垂线,垂足为
.设直线
的斜率为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/028a0c88-6000-4805-bd98-b7b0e22078cb.png?resizew=191)
(1)若直线
平分线段
,求
的值;
(2)当
时,求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/d80b861ba40387cb2bcd04945f5a371a.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/5963abe8f421bd99a2aaa94831a951e9.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/028a0c88-6000-4805-bd98-b7b0e22078cb.png?resizew=191)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
12-13高二·全国·课后作业
名校
5 . 已知
,
是圆:
(
为圆心)上一动点,线段
的垂直平分线交
于点
,求动点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f9b27de8a6165731c2bb5f6acdd551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b504a33441a3529c2dbc71412d276483.png)
![](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/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2020-12-07更新
|
488次组卷
|
9卷引用:2012-2013学年上海市金山中学高二上学期期末考试数学试卷
(已下线)2012-2013学年上海市金山中学高二上学期期末考试数学试卷上海市延安中学2015-2016学年高二上学期期末数学试题(已下线)2012年苏教版高中数学选修2-1 2.2椭圆练习卷湖南省益阳市箴言中学2018-2019学年高二上学期期中考试数学(文)试题内蒙古杭锦后旗奋斗中学2019-2020学年高二上学期第一次月考数学试题(已下线)专题49 椭圆、双曲线、抛物线(同步练习)-2021年高考一轮数学(文)单元复习一遍过(已下线)专题52 椭圆、双曲线、抛物线(同步练习)-2021年高考一轮数学(理)单元复习一遍过沪教版(2020) 选修第一册 领航者 第2章 2.2椭圆 第1课时 椭圆的标准方程人教B版(2019) 选修第一册 北京名校同步练习册 第二章 平面解析几何初步 2.5椭圆 2.5.1椭圆及其标准方程(二)
名校
解题方法
6 . 定义:由椭圆的两个焦点和短轴的一个顶点组成的三角形称为该椭圆的“特征三角形”;如果两个椭圆的“特征三角形”是相似的,则称这两个椭圆是“相似椭圆”,并将三角形的相似比称为椭圆的相似比,已知椭圆
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/18b158b9-7002-45d2-bb99-ca1f095c30c7.png?resizew=230)
(1)若椭圆
,判断
与
相似?如果相似,求出
与
的相似比;如果不相似,请说明理由;
(2)写出与椭圆
相似且焦点在
轴上,短半轴长为
的椭圆
的标准方程;若在椭圆
上存在两点
、
关于直线
对称,求实数
的取值范围;
(3)如图:直线
与两个“相似椭圆”
和
分别交于点
和点
,试在椭圆
和椭圆
上分别作出点
和点
(非椭圆顶点),使
和
组成以
为相似比的两个相似三角形,写出具体作法.(不必证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/18b158b9-7002-45d2-bb99-ca1f095c30c7.png?resizew=230)
(1)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57107d9f1e8d80a2e83df93e2891e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/b1241216f3c1cb5e73043dd1037f556d.png)
(2)写出与椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca18c89c398b435447b1970f6f00a43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca18c89c398b435447b1970f6f00a43.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/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)如图:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f326db309ab6bf16acfab03080650c73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9265fd631c3099bcb84bbb8e12fc61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8425c2d3807198fd586a2b0007179c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df7626240940eb340420a605e95aeee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2020-02-29更新
|
282次组卷
|
4卷引用:2014-2015学年上海市金山中学高二下学期期末考试数学试卷
2014-2015学年上海市金山中学高二下学期期末考试数学试卷上海市东昌中学2019-2020学年高二上学期期末数学试题上海市上海交通大学附属中学2015-2016学年高二上学期期末数学试题(已下线)专题5.8 期末考前选做30题(解答题压轴版)-2020-2021学年高二数学下学期期末专项复习(沪教版)
真题
名校
7 . 如图, 直线
与抛物线
交于
两点, 线段
的垂直平分线与直线
交于
点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/1a8c26a4-f754-47ec-ab76-845797d1a6e2.png?resizew=196)
(1)求点
的坐标;
(2)当P为抛物线上位于线段
下方(含
)的动点时, 求ΔOPQ面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d585d2d6643471640905d234d9538c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4426e9aac21e8b4bfc2b5ced1325ef.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/3582caa8f1ea0b0be9006f819e050cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/1a8c26a4-f754-47ec-ab76-845797d1a6e2.png?resizew=196)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)当P为抛物线上位于线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
您最近一年使用:0次
2019-10-02更新
|
1029次组卷
|
5卷引用:2015-2016学年上海市金山中学高二上学期期末考试数学试卷
8 . 设椭圆
的长半轴长为
,短半轴长为
,椭圆
的长半轴长为
,短半轴长为
,若
,则称椭圆
与椭圆
是相似椭圆.已知椭圆
,其左顶点为
,右顶点为
.
(1)设椭圆
与椭圆
是“相似椭圆”,求常数
的值;
(2)设椭圆
,过
作斜率为
的直线
与椭圆
仅有一个公共点,过椭圆
的上顶点
作斜率为
的直线
与椭圆
只有一个公共点,当
为何值时,
取得最小值,试求出最小值;
(3)已知椭圆
与椭圆
是相似椭圆,椭圆
上异于
的任意一点
,求证:
的垂心
在椭圆
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd731967bb86ddf18e9e473daa96041a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff1455a4045eb93f482c0751840aea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d56cbbfc76e5d203ea5efffbbc6d291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
(2)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d6ba128a26fe49c989ba5f6538e5f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4489d9b83072184c0e1d6b09be50ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0b669ef4514f24ee09adeff7f41238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d1e1062878dcb155964639267bdedf.png)
(3)已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1217c64cc23489dccb61d90a5500da84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b77e6b117cf9d90d7d31d7ebde3dbf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2017-03-03更新
|
1165次组卷
|
5卷引用:上海市金山中学2016-2017学年高二下学期期末考试数学试题
上海市金山中学2016-2017学年高二下学期期末考试数学试题2016-2017学年山东省烟台市高二上学期期末考试数学(理)试卷(已下线)山东省烟台市2016-2017学年高二上学期期末考试理数试题(已下线)专题5.8 期末考前选做30题(解答题压轴版)-2020-2021学年高二数学下学期期末专项复习(沪教版)2016届上海市浦东新区高三综合练习(三模)数学试题
名校
9 . 对于曲线
,若存在非负实数
和
,使得曲线
上任意一点
,
恒成立(其中
为坐标原点),则称曲线
为有界曲线,且称
的最小值
为曲线
的外确界,
的最大值
为曲线
的内确界.
(1)写出曲线
的外确界
与内确界
;
(2)曲线
与曲线
是否为有界曲线?若是,求出其外确界与内确界;若不是,请说明理由;
(3)已知曲线
上任意一点
到定点
的距离之积为常数
,求曲线
的外确界与内确界.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912af898055c5dabdf767a3cf7b2d8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757d9d3f6fca9391b2960775e35933c6.png)
![](https://img.xkw.com/dksih/QBM/2015/3/27/1572045010870272/1572045016965120/STEM/0fd594abc8804470b099b2dadc6a49dc.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb44db1dc864ff4901be1e10da79747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e93d8fb77f5bd2c0fc690752dfd771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3a7b671b5150b7541105a87c84540c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb44db1dc864ff4901be1e10da79747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e93d8fb77f5bd2c0fc690752dfd771.png)
(2)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777f24fed681c4b2b28349fa8325ac99.png)
(3)已知曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f49644cd9fa4688cc3a74a234952530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ec1e326713ddcd6dd66a24a809bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2016-12-03更新
|
1141次组卷
|
3卷引用:上海市金山中学2015-2016学年高二下学期期末数学试题
13-14高二下·上海金山·期末
10 . 下图是利用计算机作图软件在直角坐标平面
上绘制的一列抛物线和一列直线,在焦点为
的抛物线列
中,
是首项和公比都为
的等比数列,过
作斜率2的直线
与
相交于
和
(
在
轴的上方,
在
轴的下方).
证明:
的斜率是定值;
求
、
、
、
、
所在直线的方程;
记
的面积为
,证明:数列
是等比数列,并求所有这些三角形的面积的和.
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/b1fdd5907c8945daa1d2a6c5f85cff33.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/e5bc5a88b190402ea0a5585796983893.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/480e1c5e5b41471fb3cbb691b8dd760c.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/254ded389dcb47029ef772c5050ecdb8.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/9d29b9adb3cd4d17863ebcba6f543736.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/e5bc5a88b190402ea0a5585796983893.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/900a3ffa563046c689438590dba753a8.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/a564e5d460ff45f084c9f06f50d168aa.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/25671a533b2f49da9491f03489380d64.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/422941d4ca564a3a9450487377c153fa.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/25671a533b2f49da9491f03489380d64.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/5c35b050df974373881b650ad5208d3f.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/422941d4ca564a3a9450487377c153fa.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/5c35b050df974373881b650ad5208d3f.png)
证明:
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/ee9191fbd491406bb810d9de498be548.png)
求
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/d5fd4eafdb57476fa2e30c7b9df32b1c.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/194610503a754b7686aa315734c59db2.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/ff5ec7535416488e8cc40f3416673c07.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/25671a533b2f49da9491f03489380d64.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/ff5ec7535416488e8cc40f3416673c07.png)
记
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/4899235549084d7b8c01254c4f1bc148.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/e506fc2c8bb4417f818d405cf4ed084b.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/c8fdf56ddd71474da71fa61f9cd63e63.png)
![](https://img.xkw.com/dksih/QBM/2014/10/8/1571870225850368/1571870231740416/STEM/f9a43993371a48cfa376a82c6752a9ed.png)
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