1 . 在平面直角坐标系
中,已知椭圆
的离心率为
,且椭圆
短轴的一个顶点到左焦点
的距离等于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/7b121abd-0a84-4905-aed8-dd148b0b6048.png?resizew=235)
(1)求椭圆
的方程;
(2)设经过点
的直线
交椭圆
于
两点,弦
的中垂线
交
轴于点
.
①求实数
的取值范围;
②若
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](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/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/7b121abd-0a84-4905-aed8-dd148b0b6048.png?resizew=235)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2da6ef88591589f330304297d3abfcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f4ea4bc4c655fd337f8bdd18c493b5.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c7613bc5c3fc3d8d20b8652fedc736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
名校
2 . 已知命题
直线
与焦点在
轴上的椭圆
无公共点,命题
方程
表示双曲线.
(1)若命题
是真命题,求实数
的取值范围;
(2)若命题
是命题
的充分不必要条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e892e5d2765a48905e42a4409537af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b463851c9eb87f5b7d78b8051996c3.png)
(1)若命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2020-03-29更新
|
674次组卷
|
8卷引用:江苏省南通市2019-2020学年高二上学期教学质量调研(二)数学试题
江苏省南通市2019-2020学年高二上学期教学质量调研(二)数学试题福建省莆田第二十四中学2019-2020学年高二下学期期中测试数学(文)试题福建省莆田第二十四中学2019-2020学年高二下学期返校测试数学(文)试题甘肃省张掖市高台县第一中学2019-2020学年高二下学期期中考试数学(文)试题湖北省黄冈市黄梅国际育才高级中学2019-2020学年高二下学期期中数学试题湖北省黄石市第二中学2020-2021学年高二上学期期末数学试题安徽省马鞍山市第二中学郑蒲港分校2020-2021学年高二下学期入学摸底测试文科数学试题(已下线)高二数学下学期开学摸底卷(测试范围:选修一+选修二)-2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)
名校
解题方法
3 . 已知抛物线
的准线过椭圆C:
(a>b>0)的左焦点F,且点F到直线l:
(c为椭圆焦距的一半)的距离为4.
(1)求椭圆C的标准方程;
(2)过点F作直线与椭圆C交于A,B两点,P是AB的中点,线段AB的中垂线交直线l于点Q.若
,求直线AB的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa5d6092f598c7da4796f965e40525a.png)
(1)求椭圆C的标准方程;
(2)过点F作直线与椭圆C交于A,B两点,P是AB的中点,线段AB的中垂线交直线l于点Q.若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56cdde456a60ce63f178e9869fb723f2.png)
您最近一年使用:0次
2020-03-20更新
|
347次组卷
|
3卷引用:江苏省南通市海安高级中学2019-2020学年高二下学期3月线上考试数学试题
名校
解题方法
4 . 设椭圆
,其长轴长是短轴长的
倍,过焦点且垂直于
轴的直线被椭圆截得的弦长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/a0cedf34-9218-4baa-a292-edc5091c291f.png?resizew=219)
(1)求椭圆
的方程;
(2)点
是椭圆
上横坐标大于
的动点,点
在
轴上,圆
内切于
,试判断点
在何位置时
的长度最小,并证明你的判断.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/a0cedf34-9218-4baa-a292-edc5091c291f.png?resizew=219)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12eb814bb12c2e8d3c6de69a73e972ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6316e0e6da742e9b035d8f2cc91a4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8c7c8c8702adfbd6bcacc94a6bc661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2020-03-17更新
|
168次组卷
|
2卷引用:江苏省南通市海安高级中学2017-2018学年高二上学期期中数学(理)试题
名校
5 . 已知点
在椭圆
上,动点
都在椭圆上,且直线
不经过原点
,直线
经过弦
的中点.
(1)求椭圆
的方程;
(2)求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3178e2296170fb2ba5ed2c016a1edc80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d50d76b45349532f9b7d016c1429b1.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2020-01-15更新
|
1913次组卷
|
6卷引用:江苏省南通市通州区西亭高级中学2020-2021学年高二上学期第一次阶段检测数学试题
江苏省南通市通州区西亭高级中学2020-2021学年高二上学期第一次阶段检测数学试题黑龙江省牡丹江市爱民区第三高级中学2019-2020学年高二上学期期末数学(文)试题湖北省武汉市钢城第四中学2020-2021学年高二上学期期中数学试题专题2.7 平面解析几何(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)(已下线)重难点01:直线与椭圆的位置关系(分层练习)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)(已下线)3.1.2 椭圆的简单几何性质【第三课】“上好三节课,做好三套题“高中数学素养晋级之路
6 . 已知直线y=kx+1与焦点在x轴上的椭圆
1(b>0)总有公共点,则b的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1b3c52e6d9fc6ca5befd8b84ca560a.png)
A.[1,4) | B.(1,+∞) | C.[1,+∞) | D.[1,2) |
您最近一年使用:0次
名校
7 . 已知椭圆
的左、右顶点分别为
,点
为椭圆
上不同于
两点的动点,若直线
斜率的取值范围是
,则直线
斜率的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90b5ed62c5d6de50354a183c46be03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/185af3f2d9835aa76aeebe02875ecae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-10-26更新
|
1762次组卷
|
8卷引用:江苏省南通市如东高级中学、栟茶中学等四校2019-2020学年高二上学期期中数学试题
江苏省南通市如东高级中学、栟茶中学等四校2019-2020学年高二上学期期中数学试题吉林省长春市实验中学2019-2020学年高二上学期10月月考数学(理)试题广东省汕尾市2018-2019学年高二下学期教学质量检测数学文科试题江西省上高二中2020-2021学年高二上学期第一次月考数学(文)试题(已下线)【新教材精创】2.8+直线与圆锥曲线的位置关系(2)-A基础练-人教B版高中数学选择性必修第一册江苏省镇江一中2020-2021学年高二上学期10月月考数学试题(已下线)2019年11月8日 《每日一题》一轮复习数学(理)-直线与椭圆的位置关系(已下线)2019年11月15日 《每日一题》一轮复习文数-直线与椭圆的位置关系(1)
名校
8 . 某学校决定在主干道旁边挖一个半椭圆形状的小湖,如图所示,AB=4,O为AB的中点,椭圆的焦点P在对称轴OD上,M、N在椭圆上,MN平行AB交OD与G,且G在P的右侧,△MNP为灯光区,用于美化环境.
(1)若学校的另一条道路EF满足OE=3,tan∠OEF=2,为确保道路安全,要求椭圆上任意一点到道路EF的距离都不小于
,求半椭圆形的小湖的最大面积:(椭圆
(
)的面积为
)
(2)若椭圆的离心率为
,要求灯光区的周长不小于
,求PG的取值范围.
(1)若学校的另一条道路EF满足OE=3,tan∠OEF=2,为确保道路安全,要求椭圆上任意一点到道路EF的距离都不小于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](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/3218d9fbe87452c00739ca1883d6060e.png)
(2)若椭圆的离心率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d52429c8324350309f77e7209a5c35.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/1f4e7004-09ac-421b-9fc3-333f7ec90e7a.png?resizew=222)
您最近一年使用:0次
9 . 如图,在平面直角坐标系
中,椭圆
的左右顶点分别是
,
为直线
上一点(
点在
轴的上方),直线
与椭圆的另一个交点为
,直线
与椭圆的另一个交点为
.
(1)若
的面积是
的面积的
,求直线
的方程;
(2)设直线
与直线
的斜率分别为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0299a5a521d47c26bcc15ffa6f5218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4e4c7a79d9d3cdb9ac5949d53e33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c77b897297ddd7bd696548fbd22858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66100561b2edec283e5c45b40af439bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8350b1d4296fd6ff5fa2f58d0cf70df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cfa1e7ffae662aefb49a44c52d4954d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80861c13bb2d470a2953bebc5e3ea044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940eaf88efad6ce0781c017b8eb04bf7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/2092dd71-cab6-4921-8b8b-37840a4bdf41.png?resizew=205)
您最近一年使用:0次
10 . 如图,在平面直角坐标系
中,椭圆
的左右顶点分别是
,
为直线
上一点(
点在
轴的上方),直线
与椭圆的另一个交点为
,直线
与椭圆的另一个交点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/a7d8957b-063c-433f-b887-5a913b7c0387.png?resizew=222)
(1)若
的面积是
的面积的
,求直线
的方程;
(2)设直线
与直线
的斜率分别为
,求证:
为定值;
(3)若
的延长线交直线
于点
,求线段
长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160c9384bc59823fb52ef7bf827a2f08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed975b208f450561365bab8a7699f9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61620a272dada8d4b9a9fab6379dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/a7d8957b-063c-433f-b887-5a913b7c0387.png?resizew=222)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1fcee9e91b9bdd4665803e36a9a596b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0c821fe9c60965c45b16fc7761f9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eff998d034284391ca064755fa6bf1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61620a272dada8d4b9a9fab6379dfd.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1165830b314a0dab65ea267e82bd3f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe0ea445fc6b756b34b56a95e4d0381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b99dec26135f0631d118b84a3e75972.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971b23e3ee827018557d6c88edd5369a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
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