名校
解题方法
1 . 设椭圆
的左顶点为
,右顶点为
,已知椭圆
的离心率为
,且以线段
为直径的圆被直线
所截的弦长为
.
(1)求椭圆的方程;
(2)记椭圆
的右焦点为
,过点
且斜率为
的直线交椭圆于
两点.若线段
的垂直平分线与
轴交于点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698d7ad4f0b131f8287883ed42f79fbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
(1)求椭圆的方程;
(2)记椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd357b09ef893323574d0173152be6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2020-06-24更新
|
216次组卷
|
3卷引用:江西省萍乡市芦溪中学2022届高三上学期第二次段考数学(理)试题
2 . 已知椭圆C:
(
)经过
,
两点.O为坐标原点,且
的面积为
.过点
且斜率为k(
)的直线l与椭圆C有两个不同的交点M,N,且直线
,
分别与y轴交于点S,T.
(Ⅰ)求椭圆C的方程;
(Ⅱ)求直线l的斜率k的取值范围;
(Ⅲ)设
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c09615735d331befd07664aa47cb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
(Ⅰ)求椭圆C的方程;
(Ⅱ)求直线l的斜率k的取值范围;
(Ⅲ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cfc9b28711b4e9c4b554202fe46fe6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bd0693e932eb65b222f3453e04280b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
2020-06-23更新
|
1316次组卷
|
8卷引用:江苏省苏州市常熟中学2019-2020学年高一(15.16班)下学期六月质量检测数学试题
解题方法
3 . 已知椭圆
过点
,
分别为椭圆C的左、右焦点且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/bc8d2ac0-fbb5-4154-b55d-353165a57a56.png?resizew=229)
(1)求椭圆C的方程;
(2)过P点的直线
与椭圆C有且只有一个公共点,直线
平行于OP(O为原点),且与椭圆C交于两点A、B,与直线
交于点M(M介于A、B两点之间).
(i)当
面积最大时,求
的方程;
(ii)求证:
,并判断
,
的斜率是否可以按某种顺序构成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8989cd07bd3d5f89627c3acb24c0a462.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/bc8d2ac0-fbb5-4154-b55d-353165a57a56.png?resizew=229)
(1)求椭圆C的方程;
(2)过P点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb53c7cc8aac84b2ae3ef769bb46adb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
您最近一年使用:0次
2020-06-11更新
|
1703次组卷
|
7卷引用:山东省泰安市2020-2021学年高三上学期1月月考数学试题
山东省泰安市2020-2021学年高三上学期1月月考数学试题山东省潍坊市2020届高三模拟(二模)数学试题山东省平邑县第一中学2020届高三下学期第八次调研考试数学试题(已下线)数学-6月大数据精选模拟卷03(上海卷)(满分冲刺篇)(已下线)专题十 平面解析几何-山东省2020二模汇编(已下线)专题21 椭圆、双曲线、抛物线的几何性质的应用(讲)-2021年高三数学二轮复习讲练测(新高考版)(已下线)专题25 椭圆、双曲线、抛物线的几何性质的应用(讲)-2021年高三数学二轮复习讲练测(文理通用)
名校
解题方法
4 . 已知从圆
上一点
作两条互相垂直的直线与椭圆
相切,同时圆
与直线
交于
,
两点,则
的最小值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d08892c040ee46f86295892c35a20995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2116970e8dc7591a7881a9ef3861157a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44d9aa2005290096f91558ff399ca7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30aa2540099230e48838ca4978897fc.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/aaff41080fdea43eea7efedf9ebc1498.png)
A.![]() | B.4 | C.![]() | D.8 |
您最近一年使用:0次
2020-05-13更新
|
679次组卷
|
4卷引用:天一大联考2019-2020学年高三毕业班阶段性测试(五)文科数学试题
名校
解题方法
5 . 已知椭圆
,直线
,若椭圆C上存在两点关于直线l对称,则m的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfa8e3d36d88de8c35ac6182e58d767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-02-27更新
|
774次组卷
|
8卷引用:河北省2019-2020学年高三下学期名优校联考数学(文)试题
河北省2019-2020学年高三下学期名优校联考数学(文)试题河北省秦皇岛市抚宁区第一中学2019-2020学年高二下学期4月线上考试数学(理)试题河南省南阳市宛城区2022-2023学年高二上学期第二次月考数学试题新疆乌鲁木齐市第十二中学2024届高三下学期5月月考数学试题陕西省西安市2019-2020学年高二上学期期末数学(理)试题陕西省西安市远东一中2019-2020学年高二上学期期末数学(理)试题(已下线)解密12 圆锥曲线中的热点问题(分层训练)-【高频考点解密】2021年新高考数学二轮复习讲义+分层训练(已下线)9.3 椭圆(精练)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)
名校
解题方法
6 . 已知
是椭圆
上两个不同点,且满足
,则
的最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4daf40bad1cc89311930cce356672354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2db3534aaf21bbc27448be9ee90a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c384a2a6ec461884851651c72b94bc89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c97a75d30c9f7a72ab4e70b1f0f6dd0.png)
A.![]() | B.4 | C.![]() | D.![]() |
您最近一年使用:0次
2020-02-12更新
|
1138次组卷
|
8卷引用:四川省棠湖中学2019-2020学年高二下学期第一次在线月考数学(理)试题
四川省棠湖中学2019-2020学年高二下学期第一次在线月考数学(理)试题四川省南充高级中学2019-2020学年高二下学期3月线上月考数学(文)试题浙江省杭州市七县区2019-2020学年高二上学期期末数学试题(已下线)【新东方】新东方高二数学试卷303(已下线)【新东方】新东方高二数学试卷295(已下线)10练-冲刺2020年高考数学小题狂刷卷(浙江专用)(已下线)2.2 椭圆(提高练)-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)(已下线)二轮拔高卷08-【赢在高考·黄金20卷】备战2022年高考数学模拟卷(新高考专用)
名校
解题方法
7 . 在平面直角坐标系
中,四个点
,
,
,
中有3个点在椭圆
:
上.
(1)求椭圆
的标准方程;
(2)过原点的直线与椭圆
交于
,
两点(
,
不是椭圆
的顶点),点
在椭圆
上,且
,直线
与
轴、
轴分别交于
、
两点,设直线
,
的斜率分别为
,
,证明:存在常数
使得
,并求出
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee70f80d9b2a8a39a2e70e281d48c91e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ca4a8481029b98c0ffdd2cc5820ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea20370e5f7f00779dc1b1821986c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe44fc04812c2b7b1f423b32697b5a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过原点的直线与椭圆
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.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/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bc0ee0a95fab04edf648026f14b9ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2020-02-10更新
|
398次组卷
|
4卷引用:四川省棠湖中学2019-2020学年高二下学期第一次在线月考数学(文)试题
名校
8 . 在直角坐标系
中,已知圆
与直线
相切,点A为圆
上一动点,
轴于点N,且动点满足
,设动点M的轨迹为曲线C.
(1)求曲线C的方程;
(2)设P,Q是曲线C上两动点,线段
的中点为T,
,
的斜率分别为
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0928153ad46ce1946536d28ab0e0d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8084ce075d24d2d942736c1d61c72e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c6d3c0306e3b51c4c0db7d26b85b3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6dea55de27208f49cb5a213ced14d7.png)
(1)求曲线C的方程;
(2)设P,Q是曲线C上两动点,线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eac9ba606fb477550aa62db7bfa0ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b701b64f981e626fbab70c0f03b18787.png)
您最近一年使用:0次
2020-02-07更新
|
391次组卷
|
4卷引用:山西省运城市景胜中学2019-2020学年高二上学期12月月考数学(理)试题
名校
9 . 已知椭圆
的左、右焦点分别为
,
,直线l与椭圆C交于P,Q两点,且点M满足
.
(1)若点
,求直线
的方程;
(2)若直线l过点
且不与x轴重合,过点M作垂直于l的直线
与y轴交于点
,求实数t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.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/09df9c47a66277b8551ca86d1cf2c14d.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85eba786b6fa987bd73aedc54d34aed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若直线l过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2da6ef88591589f330304297d3abfcb.png)
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2020-02-01更新
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415次组卷
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3卷引用:2020届广东省深圳市高三上学期第二次教学质量检测数学(理)试题
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解题方法
10 . 已知椭圆C:
1(a>b>0)的两个焦点分别为F1(-1,0),F2(1,0),且椭圆C经过点P
.
(1)求椭圆C的离心率;
(2)设过点A(0,2)的直线l与椭圆C交于M,N两点,点Q是线段MN上的点,且
=
+
,求点Q的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd4fd9bfd38c5361d55735bfe4bb2d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85202445c4cb4a666d0f0c9d7d7ccd19.png)
(1)求椭圆C的离心率;
(2)设过点A(0,2)的直线l与椭圆C交于M,N两点,点Q是线段MN上的点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3dc0fd9804b3515889d63a8eb4e977b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11863b2e28904a84b5ca703b06f2f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7536a07d8175c949495611eef8c9043d.png)
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2020-12-06更新
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2032次组卷
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13卷引用:天津市耀华中学2018届高三上学期第一次月考数学(理)试题2
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