2014·江西·三模
名校
解题方法
1 . 已知椭圆
的离心率为
,以原点O为圆心,椭圆的短半轴长为半径的圆与直线
相切.
(1)求椭圆C的标准方程;
(2)若直线
与椭圆C相交于A,B两点,且
.求证:
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38f9106cef0b638e62c90afc1c523cd.png)
(1)求椭圆C的标准方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd386bcd21aebfe5e25ba23a8fab7ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
2021-01-27更新
|
284次组卷
|
7卷引用:2016-2017学年湖北省重点高中联考协作体高二下学期期中考试数学(理)试卷
2016-2017学年湖北省重点高中联考协作体高二下学期期中考试数学(理)试卷黑龙江省宾县一中2019-2020学年高二上学期第一次月考数学(文)试卷(已下线)2014届江西师大附中高三三模数学文科数学试卷(已下线)2014届甘肃省兰州一中高考模拟一文科数学试卷2016届河北省正定中学高三上第五次月考理科数学试卷新疆乌鲁木齐市第七十中学2020-2021学年高二上学期期末考试数学(理)试题山东省潍坊市安丘市2022-2023学年高二上学期期末数学试题
名校
解题方法
2 . 已知椭圆C的中心在坐标原点,左顶点
,离心率
,F为右焦点,过焦点F的直线交椭圆C于P、Q两个不同的点.
(1)求椭圆C的方程;
(2)当
时,求直线PQ的方程;
(3)设线段PQ的中点在直线
上,求直线PQ的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
(1)求椭圆C的方程;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27949106df3866afcd3c9331b9160aeb.png)
(3)设线段PQ的中点在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1a686b80b8f109a929f58c2de7201d.png)
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2021-01-26更新
|
599次组卷
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4卷引用:北京市北京交通大学附属中学2020-2021学年高二上学期期中数学试题
名校
3 . 点M是椭圆
上一点,点A是椭圆C的左顶点,MO的延长线交椭圆C于点B,
是以M为直角顶点的三角形.若存在不同于点A,B的点C,D,使得
,试探究直线AB与CD的位置关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6dcc18d9649a410567ad1cf8ea81cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4b0c4b339f44bbac0e275eb0718234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12165419545996e0aaecc012470cfbd0.png)
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4 . 已知椭圆
,直线
与椭圆交于P,Q两点,设线段
的中点为M,点O为坐标原点,且
,则直线
的斜率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61efb6625b358d5e62f7fc28d230382d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7df99fe6438442a9453fc0c57fb703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-01-09更新
|
134次组卷
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2卷引用:安徽省合肥市第六中学2020-2021学年高二上学期诊断性测试数学(理)试题
名校
5 . 已知椭圆C:
(a>b>0)的左右焦点分别为F1(-c,0)和F2(c,0),上顶点为M,且△MF1F2为等边三角形,点M到左右顶点的距离之和为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/a2fcba21-0725-470a-8c9a-3c116b953510.png?resizew=270)
(1)求椭圆C的标准方程;
(2)过点F1的直线l交椭圆C于A,B两点,若以AB为直径的圆经过点F2,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbff61fe9d4e93d7cc338489d1c99c40.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/a2fcba21-0725-470a-8c9a-3c116b953510.png?resizew=270)
(1)求椭圆C的标准方程;
(2)过点F1的直线l交椭圆C于A,B两点,若以AB为直径的圆经过点F2,求直线l的方程.
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解题方法
6 . 如图,已知椭圆
的左焦点为F,O为坐标原点,设过点F且不与坐标轴垂直的直线交椭圆于A,B两点,线段AB的垂直平分线与x轴交于点G,求点G横坐标的取值范围( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/705ea911-26a5-4700-b83d-a8fba4b2450a.png?resizew=194)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/705ea911-26a5-4700-b83d-a8fba4b2450a.png?resizew=194)
A.[-1,1] | B.![]() | C.![]() | D.(-1,0) |
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2021-01-02更新
|
128次组卷
|
2卷引用:贵州省安顺市大洋实验学校2020-2021学年高二上学期期中考试数学(理科)试题
名校
解题方法
7 . 已知椭圆
:
(
)的离心率为
,焦距为2.
(1)求椭圆
的标准方程;
(2)点
为椭圆
的上顶点,过点
作两条相互垂直的直线
,
分别与椭圆相交于
、
两点,若
,求直线
的方程.
附:多项式因式分解公式
.
![](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/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6feb482bdf3887a9fcd99145427eb09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
附:多项式因式分解公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc48eea05485b64a57e2e7a7d464b16.png)
您最近一年使用:0次
2020-12-22更新
|
100次组卷
|
2卷引用:河北省正定县第一中学2020-2021学年高二上学期期中数学试题
解题方法
8 . 已知椭圆
:
的右焦点为
,离心率为
,过原点的直线
(不与坐标轴重合)与
交于
两点,且
.
(1)求椭圆
的方程;
(2)过
作
轴于点
,连接
,并延长交椭圆
于
,证明以线段
为直径的圆经过点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.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/77969a826a095e26d60c13c6d85b369b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd263fa65347735f95d3364e5b91a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
名校
9 . 已知椭圆
的焦距与短轴长相等,过椭圆右焦点的直线
与椭圆交于
、
两点,当
与
轴垂直时,
.
(1)求椭圆
的方程;
(2)若椭圆
上存在异于
、
的一点
,使得
的重心是坐标原点
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699fc9b7e879af4866aaa07848dfb423.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若椭圆
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-12-14更新
|
192次组卷
|
2卷引用:重庆市南开中学2020-2021学年高二上学期期中数学试题
名校
解题方法
10 . 在平面直角坐标系
中,已知椭圆
:
,圆
:
,若圆
的一条切线
:
与椭圆
相交于
,
.
(1)当
,
,若
,
都在坐标轴的正半轴上,求椭圆的方程.
(2)若以
,
为直径的圆经过坐标原点,探究
,
,
之间的等量关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab035a213520a35aaa7ddf114ffbdab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798a173e5bc029fcffa0bec024a017ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若以
![](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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
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