1 . 如图,已知椭圆:
,过抛物线
:
的焦点F的直线交抛物线于M,N两点,连接NO,MO并延长分别交
于A、B两点,连接AB,
与
的面积分别记为
、
,则在下列结论中正确的为( )
A.若记直线NO,MO的斜率分别为![]() ![]() ![]() |
B.![]() ![]() |
C.设 ![]() ![]() |
D.![]() |
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2 . 已知圆:
,圆
:
,动圆
与圆
外切于点
,与圆
内切于点
圆心
的轨迹记为曲线
,则( )
A.![]() ![]() |
B.![]() ![]() |
C.![]() |
D.曲线![]() ![]() ![]() |
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解题方法
3 .
为椭圆
上一点,
为
的左、右焦点,延长
,
交
于A,B两点、在
中,记
,
,若
,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e31f17d3eae2f76500ee2e8f955865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44693396245ef7175cd2395bb2c3d95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/076f439c37c1c6fce8b2c7d10f3693ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4a3c7847e08eabac3be71b628dbfea.png)
A.![]() ![]() |
B.![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.![]() |
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解题方法
4 . 已知椭圆
的左、右焦点分别为
,
,左、右顶点分别为A,B,上顶点为D,P是E上异于A,B的一个动点,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.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/cb5b2341a3052a7afab18ac0309269c2.png)
A.E的离心率为![]() | B.直线PA与PB的斜率之积为![]() |
C.满足![]() | D.![]() |
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5 . 已知椭圆
,直线
过椭圆的左焦点
交椭圆于
两点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
A.![]() ![]() |
B.以![]() ![]() |
C.若![]() ![]() ![]() |
D.若弦![]() ![]() ![]() ![]() |
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6 . 已知椭圆
上有不同两点
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b747db7eaf469c6d1607e4b0d028299f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14436636ec6a7aec09cb63cecf6e970d.png)
A.若![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.若![]() ![]() |
D.![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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7 . 已知椭圆
左焦点
,左顶点
,经过
的直线
交椭圆于
两点(点
在第一象限),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0b4bbfa0ed04cd3c2454d99d64e29c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.若![]() ![]() ![]() |
B.![]() ![]() |
C.以![]() ![]() |
D.若直线![]() ![]() ![]() |
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8 . 已知
、
是椭圆
的左、右顶点,
是直线
上的动点(不在
轴上),
交椭圆于点
,
与
交于点
,则下列说法正确的是( )
![](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/bb76f4cf79bf0299fdc43f14fd5477e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e93309062496a9c6d3dead5a9fa59c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.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/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.![]() | B.若点![]() ![]() |
C.![]() | D.点![]() |
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9 . 如图,已知椭圆
的左、右顶点分别是
,
,上顶点为B,点P是椭圆上的一点(不同于
,
),直线
与直线
交于点M,直线
交直线
于点G(O是坐标原点),记直线
,
的斜率分别为
,
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/6f69cabc-b344-4446-a984-25781dd7df40.jpg?resizew=179)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80b861ba40387cb2bcd04945f5a371a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/6f69cabc-b344-4446-a984-25781dd7df40.jpg?resizew=179)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() |
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名校
解题方法
10 . 已知椭圆
分别为它的左右焦点,
分别为它的左右顶点,点
是椭圆上的一个动点,下列结论中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbaadaa9ace3f296ebe124dcd6032a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.存在![]() ![]() |
B.![]() ![]() |
C.直线![]() ![]() ![]() |
D.![]() ![]() |
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