1 . 折纸又称“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:用圆形纸片,按如下步骤折纸(如下图),
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/b73cd644-61d8-4b20-918e-c5af041591e8.png?resizew=181)
步骤1:设圆心是
,在圆内不是圆心处取一点,标记为F;
步骤2:把纸片对折,使圆周正好通过F;
步骤3:把纸片展开,于是就留下一条折痕;
步骤4:不停重复步骤2和3,能得到越来越多条的折痕.
所有这些折痕围成的图形是一个椭圆.若取半径为4的圆形纸片,设定点
到圆心
的距离为2,按上述方法折纸.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/a4d5b150-a9ff-4e68-8445-85c20b005ed8.png?resizew=398)
(1)建立适当的坐标系,求折痕围成椭圆的标准方程;
(2)求经过
,且与直线
夹角为
的直线被椭圆截得的弦长.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/b73cd644-61d8-4b20-918e-c5af041591e8.png?resizew=181)
步骤1:设圆心是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
步骤2:把纸片对折,使圆周正好通过F;
步骤3:把纸片展开,于是就留下一条折痕;
步骤4:不停重复步骤2和3,能得到越来越多条的折痕.
所有这些折痕围成的图形是一个椭圆.若取半径为4的圆形纸片,设定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/a4d5b150-a9ff-4e68-8445-85c20b005ed8.png?resizew=398)
(1)建立适当的坐标系,求折痕围成椭圆的标准方程;
(2)求经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecff6005f926665a926c07ad62e0f032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
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2020-11-15更新
|
385次组卷
|
3卷引用:上海市复旦大学附属中学2020-2021学年高二上学期期中数学试题
2 . 动圆
与定圆
相内切,且过点
,求动圆圆心
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f010f2af491104f58dacd27f1490098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e10de2c38bc918ae9e1ce62a5c70099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2020-06-25更新
|
757次组卷
|
4卷引用:沪教版(上海) 高二第二学期 新高考辅导与训练 第12章 圆锥曲线 12.3 椭圆的标准方程
沪教版(上海) 高二第二学期 新高考辅导与训练 第12章 圆锥曲线 12.3 椭圆的标准方程吉林省长春市第一五一中学2020-2021学年高二上学期第一次月考数学试题(希望班)吉林省长春市第一五一中学2020-2021学年高二上学期第一次月考数学试题(普通班)(已下线)专题2.3 椭圆(A卷基础篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教B版)
名校
3 . 已知椭圆
(
)的右焦点为
,
为坐标原点,点
是椭圆在第一象限的一点,且
为等边三角形,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.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/2ba7de0a0e94dab4d492558d5d39548c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
您最近一年使用:0次
2020-06-25更新
|
793次组卷
|
5卷引用:2020届上海市长宁区高三三模数学试题
2020届上海市长宁区高三三模数学试题(已下线)课时36 椭圆-2022年高考数学一轮复习小题多维练(上海专用)(已下线)专题09 椭圆、双曲线与抛物线的几何性质-2020年高考数学(文)母题题源解密(全国Ⅱ专版)(已下线)专题08 椭圆、双曲线与抛物线的几何性质-2020年高考数学(理)母题题源解密(全国Ⅱ专版)辽宁省抚顺市第二中学2020-2021学年高三上学期全真模拟考试数学试题
名校
解题方法
4 . 已知椭圆
两焦点
,并经过点
.
(1)求椭圆
的标准方程;
(2)设
为椭圆
上关于
轴对称的不同两点,
为
轴上两点,且
,证明:直线
的交点
仍在椭圆
上;
(3)你能否将(2)推广到一般椭圆中?写出你的结论即可.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f49644cd9fa4688cc3a74a234952530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8ae763010ec2babfa828d264ace7fc.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0200bb2c3cc080a5d1ecf36f80aea0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b46051fea24610b42da314ec58bbb80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142eefc20e0a5ab44d56d38ca442ae16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(3)你能否将(2)推广到一般椭圆中?写出你的结论即可.
您最近一年使用:0次
5 . 已知双曲线
的两焦点为
,
为动点,若
.
(1)求动点
的轨迹
方程;
(2)若
,设直线
过点
,且与轨迹
交于
两点,直线
与
交于
点.试问:当直线
在变化时,点
是否恒在一条定直线上?若是,请写出这条定直线方程,并证明你的结论;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea74737939c0f94c91229a7098f36ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f595683f69d5d6b5ca76408b0ff6ff17.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b5dbfa1543e19099e728ca895a3146.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f31a1284206d3a2fdea63f2a6983b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c45a57242b7e27503239c428b773f6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec18c028746b73be7503ff6ff458a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
名校
解题方法
6 . 椭圆
的一个焦点是
,动点
是椭圆上的点,以线段
为直径的圆始终与一定圆相切,则定圆的方程是_________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
您最近一年使用:0次
2020-02-29更新
|
493次组卷
|
3卷引用:上海市七宝中学2019-2020学年高二上学期期末数学试题
名校
解题方法
7 . 已知两点
、
,动点
满足
,记
的轨迹为曲线
,直线
(
)交曲线
于
、
两点,点
在第一象限,
轴,垂足为
,连结
并延长交曲线
于点
.
(1)求曲线
的方程,并说明曲线
是什么曲线;
(2)若
,求△
的面积;
(3)证明:△
为直角三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45349f54f6abc8d331556557255f024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996dadd8544543637bd2d32a1f79579e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b549d39d7e273f5ba461f1d508b20dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3016baf1a9ce777f16ea9ce469b2510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae95e96ce568efee50145f8d017353df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3d566704b44ea4ef1f99c37bd46902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e69866076dcff686a05e9e91e61e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec215f280523d64b9dc3f4d03724cf2.png)
(3)证明:△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec215f280523d64b9dc3f4d03724cf2.png)
您最近一年使用:0次
8 . 平面内任意一点
到两定点
、
的距离之和为
.
(1)若点
是第二象限内的一点且满足
,求点
的坐标;
(2)设平面内有关于原点对称的两定点
,判别
是否有最大值和最小值,请说明理由?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13683e2ecf2164a0adbfdb9923d210a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8786e2332514282b5b2e1d8b6aeb7d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设平面内有关于原点对称的两定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfc9cfb1d1c8578ac3566490132bc7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2241927e706ebd00e1c9adf0cc065b8.png)
您最近一年使用:0次
2020-01-13更新
|
358次组卷
|
4卷引用:上海市奉贤区2019-2020学年高三上学期第一次模拟考试(期末)数学试题
上海市奉贤区2019-2020学年高三上学期第一次模拟考试(期末)数学试题(已下线)课时36 椭圆-2022年高考数学一轮复习小题多维练(上海专用)(已下线)第13讲 椭圆 - 1沪教版(2020) 一轮复习 堂堂清 第七单元 7.9 曲线与方程
名校
9 . 在直角坐标系
中,点
到两点
,
的距离之和为4,设点
的轨迹为
,直线
与轨迹
交于
两点.
(1)求出轨迹
的方程;
(2)若
,求弦长
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e5cdcc3cf3ca21f12edaf5397ddbd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f780f4f03699023b1322a1e002539.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/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求出轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb74745f1d6a291a7422feb93c27dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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2019-11-10更新
|
1553次组卷
|
4卷引用:上海市上海师范大学附属外国语中学2018-2019学年高二上学期期末数学试题
名校
10 . 已知圆
.
(1)设点
是圆
上一点,求
的取值范围;
(2)如图,定点
,
为圆
上一动点,
的中垂线交
于点
.求证:动点
的轨迹为椭圆,并求其方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d723ec3118dcc3be5c552b3d4bda4ff5.png)
(1)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defd208a1573c26c88e0ed21c5f89ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
(2)如图,定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6ff81aedbefa935da289dc632e78eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/110594e5-236e-43e4-831a-cd5ae8de2a89.png?resizew=152)
您最近一年使用:0次