1 . 舒腾尺是荷兰数学家舒腾(1615-1660)设计的一种作图工具,如图,
是滑槽
的中点,短杆
可绕
转动,长杆
通过
处的铰链与
连接,
上的栓子
可沿滑槽
滑动,当点
在滑槽
内作往复移动时,带动点
绕
转动,点
也随之而运动,记点
的运动轨迹为
,点
的运动轨迹为
.若
,
,且
,过
上的点
向
作切线,则切线长的最大值为______
![](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/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54298f581688081d0b0214334a0dedf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e47bb98258ebfcf1d8ad4bac10b7ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/919e839fe46b774bfdd7e01206793d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
您最近一年使用:0次
2020高三·全国·专题练习
真题
解题方法
2 . (1)求右焦点坐标是
,且经过点
的椭圆的标准方程;
(2)已知椭圆
的方程是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
.设斜率为
的直线
,交椭圆
于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
两点,
的中点为
.证明:当直线
平行移动时,动点
在一条过原点的定直线上;
(3)利用(2)所揭示的椭圆几何性质,用作图方法找出下面给定椭圆的中心,简要写出作图步骤,并在图中标出椭圆的中心.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4b5304fcad9f2a5a355e26b2318f5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b647d7e0213e12c73db1adb33e8a10d.png)
(2)已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faa2be655f8c6db5187a1928cf8bea9.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/50312681cba520fc026f5b851c210d5e.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)利用(2)所揭示的椭圆几何性质,用作图方法找出下面给定椭圆的中心,简要写出作图步骤,并在图中标出椭圆的中心.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/4d864af0-86dc-40c6-b710-7bd08bf0cf50.png?resizew=129)
您最近一年使用:0次
2020-05-26更新
|
483次组卷
|
3卷引用:2005年普通高等学校春季招生考试数学试题(上海卷)
2005年普通高等学校春季招生考试数学试题(上海卷)(已下线)秒杀题型09 圆锥曲线中的中点弦-2020年高考数学试题调研之秒杀圆锥曲线压轴题沪教版(2020) 选修第一册 领航者 第2章 2.2椭圆 第2课时 椭圆的性质(1)
名校
3 . 对于圆
上任意一点
,
的值与x、y无关,有下列结论中正确的命题是______ (填写相应的序号).
①点
的轨迹是一个圆;
②r不存在最小值;
③当
时,r有最大值
;
④当
,
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d787ea5d978055cb757286937e5bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6853ff54c4a3be145899d16850245963.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
②r不存在最小值;
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a78aae223991954a893ea4ec42833a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45767ebe3415761178db9b024da09b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c34653ee0f201559c6086773137382.png)
您最近一年使用:0次
名校
解题方法
4 . 已知曲线C的方程为
,则下列说法正确的是______ .(填写序号)
①曲线C关于原点中心对称;
②曲线C关于直线
对称;
③若动点P、Q都在曲线C上,则线段
的最大值为3;
④曲线C的面积小于3.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dd871af23fc3f4648eee952429c068b.png)
①曲线C关于原点中心对称;
②曲线C关于直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
③若动点P、Q都在曲线C上,则线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b1113864968119e61aeee9ba9c613b.png)
④曲线C的面积小于3.
您最近一年使用:0次
名校
5 . 数学中有许多形状优美、寓意美好的曲线,曲线
就是其中之一.曲线C对应的图象如图所示,下列结论:
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261485158400/2542441775185920/STEM/b8f87e4853394f57b71cb90416bb3efa.png?resizew=132)
①直线AB的方程为:
;
②曲线C与圆
有2个交点;
③曲线C所围成的“心形”区域的面积大于12;
④曲线C恰好经过4个整点(即横、纵坐标均为整数的点).
其中正确的是:________ .(填写所有正确结论的编号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5a27e68ac82e560536b3bdefd4b08f.png)
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261485158400/2542441775185920/STEM/b8f87e4853394f57b71cb90416bb3efa.png?resizew=132)
①直线AB的方程为:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6274852e643a635e7340efa732edddc4.png)
②曲线C与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd89a03660c85fb78bd7fe82ee3068c.png)
③曲线C所围成的“心形”区域的面积大于12;
④曲线C恰好经过4个整点(即横、纵坐标均为整数的点).
其中正确的是:
您最近一年使用:0次
2020-09-04更新
|
415次组卷
|
3卷引用:上海市南洋模范中学2020-2021学年高二上学期10月月考数学试题
6 . 已知双曲线C:
定义:把双曲线
的虚轴保持不变,渐近线的斜率变为原来渐近线斜率的两倍得到的曲线称为曲线
的“
线”,把双曲线
的左支向右平移
个单位,把它的右支向左平移
个单位得到的曲线称为曲线
的“
-线”,若双曲线
是等轴双曲线,且焦距等于
,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/7/4c91a0eb-1442-46fa-bc3a-7a4cce048598.png?resizew=190)
(1)求双曲线
的“
-线”和“
-线”;
(2)若由“
-线”和“
-线”围成的封闭曲线上的点集都在圆
内或圆
上,求半径最小时圆
的方程,并在坐标系中用尺规作图画出该封闭曲线和圆
大致图像.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4446f654cf8401b640cc79c2b97af5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec978eb43bc4f9e7df83b0d0195dcda.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/7/4c91a0eb-1442-46fa-bc3a-7a4cce048598.png?resizew=190)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
(2)若由“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
7 . 城市道路大多是纵横交错的矩形网格状,从甲地到乙地的最短路径往往不是直线距离,而是沿着网格走的直角距离,在直角坐标系
中,定义点
的“直角距离”
为:
,设
.
![](https://img.xkw.com/dksih/QBM/2021/12/17/2874575813795840/2876536250466304/STEM/6a33005ce1b74a7abf2038abc4e98eca.png?resizew=426)
(1)写出一个满足
的点
的坐标;
(2)过点
作斜率为
的直线
,点
分别是直线
上的动点,求
的最小值;
(3)设
,记方程
的曲线为
,类比椭圆研究曲线
的性质(结论不要求证明),并在所给坐标系中画出该曲线;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4daf40bad1cc89311930cce356672354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4a2681390214200443ae07c01a4abe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093c6d5bcaa69cea79b24688f5d1bd97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977d395567ac7d083ee9d15626dcc36a.png)
![](https://img.xkw.com/dksih/QBM/2021/12/17/2874575813795840/2876536250466304/STEM/6a33005ce1b74a7abf2038abc4e98eca.png?resizew=426)
(1)写出一个满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3deaa808b583380da1e2dfd47c4b2daa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977d395567ac7d083ee9d15626dcc36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/162b555f0636a7638fc25feb819512ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06779a085af1299ef1fdc72e55ea3b5d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86da24b34e0ea2afb5eb98673b310355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
您最近一年使用:0次
8 . 已知曲线
.
![](https://img.xkw.com/dksih/QBM/2021/3/25/2685374732812288/2687018477101056/STEM/fa6461db-3861-4510-bcf7-70df55970bed.png?resizew=283)
(1)画出曲线C的图像;
(2)若直线
与曲线C有两个公共点,求k的取值范围;
(3)若
,Q为曲线C上的点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2342e17a0b90b9bb6e4f3e62347d103a.png)
![](https://img.xkw.com/dksih/QBM/2021/3/25/2685374732812288/2687018477101056/STEM/fa6461db-3861-4510-bcf7-70df55970bed.png?resizew=283)
(1)画出曲线C的图像;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0d6d0cfe389abca252332223b5da17.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c1e84907c4fb352a88daac7810959e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82358b724051b032c7ec734a226ae84.png)
您最近一年使用:0次
2021-03-27更新
|
186次组卷
|
3卷引用:上海市华师大三附中2021届高三下学期第一次阶段检测数学试题
9 . 我边防局接到情报,在海礁
所在直线
的一侧点
处有走私团伙在进行交易活动,边防局迅速派出快艇前去搜捕:如图,已知快艇出发位置在
的另一侧码头
处,
公里,
公里,
;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/01ae3af3-0a60-478c-a57b-834262fb6aca.png?resizew=136)
(1)是否存在点
,使快艇沿航线
或
的路程相等;如存在,则建立适当的直角坐标系,求出点
的轨迹方程,且画出轨迹的大致图形;如不存在,请说明理由;
(2)问走私船在怎样的区域上时,路线
比路线
的路程短,请说明理由.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c3f13203c1915b104924f650fe4227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54bf739ada87edb51304d38f09b46d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15b82151bff7cc0238d2034a6129f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/01ae3af3-0a60-478c-a57b-834262fb6aca.png?resizew=136)
(1)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c24a1f5dc4d939fc7f6f76cfa387f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2391f20b822ea7fdde7b37a1713699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)问走私船在怎样的区域上时,路线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c24a1f5dc4d939fc7f6f76cfa387f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2391f20b822ea7fdde7b37a1713699.png)
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