名校
解题方法
1 . 若
,
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726c078ca626f64e0d02c2666d8af105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e86a0979cb3dfd290c8ee0a94bf210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d499e8ca8a0c2c810507e34456181577.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
名校
解题方法
2 . 已知双曲线
的离心率为
,上焦点
到其中一条渐近线的距离为2.
(1)求双曲线的标准方程;
(2)过
的直线
交双曲线上支于
,
两点.在
轴上是否存在定点
,使得
恒成立?若存在,求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b26461529321c5e669bdf3c489c5d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448f5c45be5e4ee2e189204d334b83fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
(1)求双曲线的标准方程;
(2)过
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11dd223284fd91829a2a2cb96562619a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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3 . 已知椭圆
的左右焦点分别为
,
,且椭圆过点
,直线
与椭圆
相交于
,
两点.
![](https://img.xkw.com/dksih/QBM/2024/1/22/3416829436559360/3418748643033088/STEM/def8a15c98804ff0806a54bb62dd5414.png?resizew=164)
(1)求椭圆
的方程;
(2)若
不过原点且不平行于坐标轴,记线段
的中点为
,求证:直线
的斜率与
的斜率的乘积为定值;
(3)若
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c495971e4dab6f02b0a07ccd860c6d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/087f47d942fb125734a8a5fd599aa4f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a75defcf53e29d3814c4801c8ebacf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480eeb06d3e1cb6751b367a24047e384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b89ef51dc02763c03ef4d937f6386bf1.png)
![](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://img.xkw.com/dksih/QBM/2024/1/22/3416829436559360/3418748643033088/STEM/def8a15c98804ff0806a54bb62dd5414.png?resizew=164)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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4 . 直线
与抛物线
相交于
,
两点,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
A.直线![]() | B.直线![]() |
C.![]() | D.![]() |
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2024-01-25更新
|
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3卷引用:江苏省无锡市第一中学2023-2024学年高二上学期期末考试数学试题
江苏省无锡市第一中学2023-2024学年高二上学期期末考试数学试题(已下线)3.3.2 抛物线的简单几何性质【第三练】“上好三节课,做好三套题“高中数学素养晋级之路江苏省南京市田家炳高级中学2023-2024学年高二下学期期初考试数学试题
名校
解题方法
5 . 已知双曲线
左、右焦点分别为
、
,
、
为双曲线一条渐近线上的两点,
为双曲线的右顶点,若四边形
为矩形,且
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91e2ddf362dc348b6603abde27a6f84.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c482f270b5d1961f03d5a58c9912867c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ad1164f00c6c8ed67468c023541535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-25更新
|
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2卷引用:江苏省无锡市第一中学2023-2024学年高二上学期期末考试数学试题
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6 . 下列说法正确的有( )
A.“![]() ![]() |
B.命题“![]() |
C.命题“![]() ![]() |
D.“![]() ![]() ![]() |
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2024-03-01更新
|
298次组卷
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解题方法
7 . 椭圆
的离心率为
,且经过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd86f94dec7de4d01c63a43ed6744cb.png)
(1)求椭圆方程
(2)点A为椭圆的上顶点,过点
的直线l交椭圆于P,Q两点,直线AP,AQ分别交x轴于点M,N,若
,求直线l的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd86f94dec7de4d01c63a43ed6744cb.png)
(1)求椭圆方程
(2)点A为椭圆的上顶点,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e30645f36e8628b9e25d53598d5174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6dbb5fae7677efea8ea5ea5cdb369b1.png)
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2024-01-19更新
|
407次组卷
|
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解题方法
8 . 设F是双曲线
的右焦点,O为坐标原点,过F作C的一条渐近线的垂线,垂足为M,若
的内切圆与x轴切于点N,且
,则C的离心率为____________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22739043293c7c083a3d72750128307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596adce251f135fce4b2a94ffbb84b98.png)
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2023-12-22更新
|
428次组卷
|
4卷引用:江苏省无锡市2023-2024学年高二上学期期终教学质量调研测试数学试卷
(已下线)江苏省无锡市2023-2024学年高二上学期期终教学质量调研测试数学试卷云南省红河州2024届高三一模数学试题河北省衡水市安平中学2023-2024学年高二下学期开学考试数学试题 山东省青岛第五十八中学2023-2024学年高二上学期阶段性测试(第二次月考)数学试卷
名校
解题方法
9 . 如图,直三棱柱
中,
为等腰直角三角形,
,E,F分别是棱
上的点,平面
平面
,M是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/130f51e7-22c1-4148-886e-06e411f590ef.png?resizew=136)
(1)证明:
平面
;
(2)若
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d89ba4036a5d18ec4abed44d7fd8e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e86e3991200297ad172455e5ea93f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/130f51e7-22c1-4148-886e-06e411f590ef.png?resizew=136)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0684e0b09b04661c602437982c0397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d557872d3299577be8c5872ba1ae5b59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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2023-12-20更新
|
643次组卷
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4卷引用:江苏省无锡市南菁高级中学2024届高三上学期期末模拟数学试题
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10 . 设
为坐标原点,
为椭圆
的焦点,点
在
上,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.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/cfa51f6292cd2d8e922e5e4d9f813e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204196267ea8c9ec2544b3084d7952da.png)
A.![]() | B.0 | C.![]() | D.![]() |
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2023-11-09更新
|
1835次组卷
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5卷引用:江苏省无锡市南菁高级中学2024届高三上学期期末模拟数学试题
江苏省无锡市南菁高级中学2024届高三上学期期末模拟数学试题浙江省宁波市2024届高三上学期高考模拟考试数学试题江苏省常州市联盟学校2024届高三上学期12月学情调研数学试题(已下线)热点7-2 椭圆及其应用(8题型+满分技巧+限时检测)(已下线)专题07 平面解析几何