1 . ①已知点
,直线
,动点P满足到点A的距离与到直线l的距离之比为
;
②已知圆C的方程为
,直线l为圆C的切线,记点
,
到直线l的距离分别为
,
,动点P满足
,
;
③点S,T分别在x轴,y轴上运动,且
,动点P满足
;
在①,②,③这三个条件中,动点P的轨迹W为椭圆的是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d026d2298b74855ce6b9550ed60bcb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3a8183f5256dbe27e2fd7e3f4873e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
②已知圆C的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d026d2298b74855ce6b9550ed60bcb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e316143ca26461f71fa70d5322aa58dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6062d135a23e4fe8dd57b8d91ba7d994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ba05fe3ac6e219804cab6d7bcc86fe.png)
③点S,T分别在x轴,y轴上运动,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630f749216b47240e1605818d117f9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18ba7e1e77b5b31b867f7e6d2dfb577.png)
在①,②,③这三个条件中,动点P的轨迹W为椭圆的是
您最近一年使用:0次
名校
2 . 已知点D为圆O:
上一动点,过点D分别作
轴、
轴的垂线,垂足分别为A、B,连接BA并延长至点P,使得
,点P的轨迹记为曲线C .
(1)求曲线C的方程;
(2)设直线l与曲线C交于不同于右顶点Q的M,N两点,且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9e63f8aa053688faaa75be638e7c3e.png)
(1)求曲线C的方程;
(2)设直线l与曲线C交于不同于右顶点Q的M,N两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40de95d0e65c07fe954e4643a3bb6ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f07baa8b45a039974d841a2ab024d4.png)
您最近一年使用:0次
2022-05-12更新
|
504次组卷
|
2卷引用:江西省鹰潭市2022届高三第二次模拟考试数学(文)试题
3 . 设O为坐标原点,动点P在圆
上,过点P作
轴的垂线,垂足为Q且
.
(1)求动点D的轨迹E的方程;
(2)直线
与圆
相切,且直线
与曲线E相交于两个不同的点A、B,点T为线段AB的中点.线段OA、OB分别与圆O交于M、N两点,记
的面积分别为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8628837ebfe0dae84f36cce491bac8.png)
(1)求动点D的轨迹E的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaecfbde526079d21c439cc4609be723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
名校
解题方法
4 . AB是平面上长度为4的一条线段,P是平面上一个动点,且
,M是AB的中点,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888b342490558858ee69dad6f5472599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1e29bc2fd46f8905a3c230cf543c33.png)
您最近一年使用:0次
2022-04-20更新
|
1405次组卷
|
5卷引用:江西省宜春市丰城中学2022届高三5月模拟数学(理)试题
江西省宜春市丰城中学2022届高三5月模拟数学(理)试题沪教版(2020) 选修第一册 领航者 第2章 复习与小结(1)椭圆的几何性质(已下线)专题55:椭圆-2023届高考数学一轮复习精讲精练(新高考专用)(已下线)第05讲 椭圆及其性质(八大题型)(讲义)-4
解题方法
5 . 已知点T是圆
上的动点,点
,线段
的垂直平分线交线段
于点S,记点S的轨迹为曲线C.
(1)求曲线C的方程;
(2)过
作曲线C的两条弦
,
,这两条弦的中点分别为P,Q,若
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff1d71c317f1076e2e9d89f78db64a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42f05b013e4b7166cbc87c5a83d6a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf58e5fea1189b33cf55d86335452f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ec05e3cec27677ded7b4aecaa62d3.png)
(1)求曲线C的方程;
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42f05b013e4b7166cbc87c5a83d6a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca644f11d0b4f0e425065fd68cb93c27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dcc9f79fe5f07f25447aa442ee14ad.png)
您最近一年使用:0次
解题方法
6 . “工艺折纸”是一种把纸张折成各种不同形状物品的艺术活动,在我国源远流长,某些折纸活动蕴含丰富的数学内容,例如:用一张圆形纸片,按如下步骤折纸(如下图1)
步骤1:设圆心是
,在圆内异于圆心处取一点,标记为
;
步骤2:把纸片折叠,使圆周正好通过点
;
步骤3:把纸片展开,并留下一道折痕;
步骤4:不停重复步骤2和3,就能得到越来越多的折痕(如图2).
![](https://img.xkw.com/dksih/QBM/2022/3/23/2942434683338752/2943237843058688/STEM/feec7773-0846-4b91-b621-5aa3bbd07b4f.png?resizew=326)
(1)已知这些折痕所围成的图形是一个椭圆.若取半径为
的圆形纸片,设定点
到圆心
的距离为2,按上述方法折纸.以点
所在的直线为
轴,线段
的中垂线为
轴,建立坐标系,求折痕所围成的椭圆
(即图1中
点的轨迹)的标准方程.
(2)经过椭圆
的左焦点
作直线
,且直线l交椭圆
于
两点,问
轴上是否存在一点
,使得
为常数,若存在,求出
坐标及该常数,若不存在,说明理由.
步骤1:设圆心是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
步骤2:把纸片折叠,使圆周正好通过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
步骤3:把纸片展开,并留下一道折痕;
步骤4:不停重复步骤2和3,就能得到越来越多的折痕(如图2).
![](https://img.xkw.com/dksih/QBM/2022/3/23/2942434683338752/2943237843058688/STEM/feec7773-0846-4b91-b621-5aa3bbd07b4f.png?resizew=326)
(1)已知这些折痕所围成的图形是一个椭圆.若取半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b92dbe7d01d47d6c2db1396180caf76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)经过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fd3a87ff523729402741d91ec701f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
解题方法
7 . 已知圆
:
,动圆
过点
且与圆
相切,记动圆圆心
的轨迹为曲线C.
(1)求曲线C的方程;
(2)过点
的直线m交椭圆C于点M、N,且满足
(E为圆E的圆心),求直线m的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8911f31214a92bcf5a2918a83ccdf9ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求曲线C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ff5934f25c3eb2653400af26ef9f97.png)
您最近一年使用:0次
2022-01-24更新
|
627次组卷
|
3卷引用:江西省上饶市2022届高三一模数学(理)试题