1 . 已知O为坐标原点,抛物线E:
的焦点F到准线l的距离为2.
(1)求p;
(2)若A,B,C为E上不同的三点,且
,直线AB,FC分别与l交于点M,N,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
(1)求p;
(2)若A,B,C为E上不同的三点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4e9d2b511b7ef084f9cc47e0c398dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7db9b4ac9106bfaf32eba6ae265872b.png)
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2 . 如图,三棱锥
和
均为棱长为2的正四面体,且A,B,C,D四点共面,记直线AE与CF的交点为Q.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/3871b0ce-1ad6-41ea-8c43-aa42c85d1b9e.png?resizew=213)
(1)求三棱锥
的体积;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52753d89bf58589e2e83b19bd3d140b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6e3f0518632294dc748ca9710d15b7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/3871b0ce-1ad6-41ea-8c43-aa42c85d1b9e.png?resizew=213)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186fad2b458125c4bda98ab52e7ac27a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59021f53cbc379d349b42decae22d0a4.png)
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解题方法
3 . 在等比数列
中,已知
,则
是数列
有最小值为
的( )条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26129bf33c739a82bcb384dfd9a65dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
A.充分不必要 | B.必要不充分 |
C.既不充分又不必要 | D.充要 |
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2023-03-07更新
|
351次组卷
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3卷引用:江苏省南京师范大学附属中学江宁分校等2校2022-2023学年高三上学期期末联考数学试题
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4 . 反比例函数
的图象是双曲线(其渐近线分别为
轴和
轴);同样的,“对勾函数”
的图象也是双曲线.设
,则此“对勾函数”所对应的双曲线的焦距为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d6ee7b62a2eace5b3f594b6e0d516f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29de30c9ad808e2d1b6d20fb207c2d4.png)
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2023-02-23更新
|
679次组卷
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6卷引用:江苏省2024届高三上学期期末迎考数学试题
江苏省2024届高三上学期期末迎考数学试题福建省宁德市2022-2023学年高二上学期区域性学业质量检测(期末)数学试题(已下线)第一章 导数与函数的图像 专题二 函数的凹凸性与渐近线 微点2 函数的凹凸性与渐近线综合训练(已下线)大招6 对勾函数(已下线)专题8 2个二级结论速解对勾函数问题福建省龙岩市连城县第一中学2023-2024学年高二上学期月考(二)数学试题
5 . 如图,在四棱锥
中,
平面
,底面
为矩形,
分别为
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/d5f2a1df-815b-43b3-9721-2b90424e22af.png?resizew=153)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面PAD;
(2)在线段
上求点
,使得平面
与平面
夹角的余弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433330447c4947540b3dc52719659681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5a9a04de2ddcec2b2799ab5476f2c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/d5f2a1df-815b-43b3-9721-2b90424e22af.png?resizew=153)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)在线段
![](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/ed4cba9d2412e4a28f8740bddd5738d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
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解题方法
6 . 双曲线
的左、右焦点分别为
,
,过
的直线与双曲线左、右两支分别交于点P,Q,若
,M为PQ的中点,且
,则双曲线的离心率为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f702eb2e105fd3deef378d473b20f709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c68acf4eb46a0464bbd0ad635eba576.png)
A.![]() | B.![]() | C.![]() | D.2 |
您最近一年使用:0次
2023-02-15更新
|
903次组卷
|
2卷引用:江苏省无锡市2022-2023学年高三上学期期末数学试题
解题方法
7 . 已知椭圆
的右焦点F和抛物线
的焦点重合,且
和
的一个公共点是
.
(1)求
和
的方程;
(2)过点F作直线l分别交椭圆于A,B,交抛物线
于P,Q,是否存在常数
,使
为定值?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e48d1edbfb6a5a48f9a95551d1dbc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c9c87eba774f6bc072663d32d11fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5b4d0583e8b68caf2125d0b4ce6a2c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)过点F作直线l分别交椭圆于A,B,交抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc54b41f06056335b2d6a19738d23341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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8 . 已知正三棱柱
,底面边长为2,D是AC中点,若该正三棱柱恰有一内切球,下列说法正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
A.平面![]() ![]() |
B.![]() ![]() |
C.该正三棱柱体积为2 |
D.该正三棱柱外接球的表面积为![]() |
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解题方法
9 . 已知
,
为曲线
的焦点,则下列说法正确的是( ).
![](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/9a1117b02834304c418f9acfebbff5c8.png)
A.若曲线C的离心率![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
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10 . 某研究性学习小组发现,由双曲线
的两渐近线所成的角可求离心率
的大小,联想到反比例函数
的图象也是双曲线,据此可进一步推断双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bd7e92dae1e0c2af6c33d5e202f544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90678a404b0c5a139c5ed8a51be1b62.png)
A.![]() | B.2 | C.![]() | D.5 |
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