名校
解题方法
1 . 在平面直角坐标系
中,椭圆
,圆
,
为圆
上任意一点,
为椭圆
上任意一点.过
作椭圆
的两条切线
,
,当
,
与坐标轴不垂直时,记两切线斜率分别为
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f62686f6f9118291c444a8d5a4d0f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/c5db41a1f31d6baee7c69990811edb9f.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
A.椭圆![]() ![]() | B.![]() |
C.![]() ![]() | D.![]() |
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2024-06-10更新
|
1181次组卷
|
2卷引用:湖北省武汉市2024届高三下学期5月模拟训练试题数学试卷
名校
解题方法
2 . 已知椭圆
的左、右焦点分别为
,过
的直线
交椭圆
于
两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4129f43a6af21631251511e63e2ac4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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)
A.椭圆![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2024-02-04更新
|
481次组卷
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2卷引用:甘肃省2023-2024学年高二上学期1月期末学业质量监测数学试题
解题方法
3 . 设
,
为椭圆
:
的左右顶点,
,
为
的左、右焦点,点
在
上,则( )
![](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/44d12ebd10f6c0bcf98be52c32b107f1.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.当椭圆![]() ![]() ![]() |
B.在椭圆![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.若点![]() ![]() ![]() ![]() ![]() ![]() |
D.不存在点![]() ![]() |
您最近一年使用:0次
4 . 法国数学家加斯帕尔•蒙日发现:椭圆的两条互相垂直的切线的交点轨迹是以椭圆中心为圆心的圆(称为椭圆的蒙日圆).已知椭圆
的左、右焦点分别为
,左、右顶点分别为
,点
是椭圆上异于
的动点,点
是该椭圆的蒙日圆上的动点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bdca942888700310971d0e2c70e624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.该椭圆的蒙日圆的方程为![]() |
B.存在点![]() ![]() |
C.使![]() ![]() |
D.直线![]() ![]() |
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2024-01-30更新
|
263次组卷
|
2卷引用:河北省邯郸市2023-2024学年高二上学期期末质量检测数学试题
解题方法
5 . 已知F是椭圆
的右焦点,直线
与椭圆C交于A,B两点,M,N分别为
,
的中点,O为坐标原点,若
,则椭圆C的离心率可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b5d523373b8cbfa33e42a1bf154544.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-25更新
|
341次组卷
|
5卷引用:湖南省部分学校2023-2024学年高二上学期期末联合考试数学试题
湖南省部分学校2023-2024学年高二上学期期末联合考试数学试题陕西省西安市莲湖区2023-2024学年高二上学期期末质量监测数学试题广东省部分学校2023-2024学年高二上学期期末教学质量监测数学试卷(已下线)考点14 余弦定理及应用 --2024届高考数学考点总动员【练】(已下线)专题4 离心率题 定义方程 【练】
名校
解题方法
6 . 椭圆
的左、右焦点分别为
,
为坐标原点,则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.过点![]() ![]() |
B.椭圆![]() ![]() |
C.若实数![]() ![]() ![]() |
D.![]() ![]() ![]() ![]() ![]() ![]() |
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2023-12-15更新
|
102次组卷
|
2卷引用:四川省成都市石室阳安中学2023-2024学年高二上学期12月月考数学试题
解题方法
7 . 已知椭圆
的左、右焦点分别为
,过
的直线
交椭圆
于
两点(
在
的上方),
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be0160e528ddd1d2a7f20ad378879c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f331a07e220f30123c6e6f09e97b2aee.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
名校
解题方法
8 . 某学校数学课外兴趣小组研究发现:椭圆的两条互相垂直的切线交点的轨迹是以椭圆中心为圆心的圆,称为该椭圆的“蒙日圆”.利用此结论解决下列问题:已知椭圆
的离心率为
,
,
为C的左、右焦点且
,A为C上一动点,直线
.说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.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/a2644e9f73e5871db934fdafc431d675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f61419ddccecb07a725c71214a6a36d5.png)
A.椭圆C的“蒙日圆”的面积为![]() |
B.对直线l上任意点P,都有![]() |
C.椭圆C的标准方程为![]() |
D.椭圆C的“蒙日圆”的两条弦![]() ![]() |
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2023-11-20更新
|
288次组卷
|
2卷引用:江西省九江第一中学2023-2024学年高二上学期期中考试数学试卷
解题方法
9 . 已知
为椭圆
的右焦点,直线
与椭圆交于
两点,直线
与椭圆交于另一点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b747db7eaf469c6d1607e4b0d028299f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de18327660bf156f0f47dca926a97ea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() ![]() |
B.![]() |
C.![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
2023-11-16更新
|
482次组卷
|
2卷引用:浙江省浙北G2联盟2023-2024学年高二上学期期中联考数学试题
10 . 椭圆
的左右焦点分别为
,
,
为坐标原点,
为椭圆
上一点,给出以下四个命题,正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.过点![]() ![]() ![]() ![]() ![]() |
B.过点![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.椭圆![]() ![]() ![]() |
D.![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-11-09更新
|
270次组卷
|
2卷引用:河北省张家口市张垣联盟2023-2024学年高二上学期11月月考数学试题