1 . 直线
被圆
截得的弦长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8a3365e99f926b1dafa901ab232152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca23a2a8cf7f1022133ee825c7e12ae8.png)
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2024-04-10更新
|
348次组卷
|
2卷引用:北京市八一学校2021-2022学年高二上学期12月月考数学试卷
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2 . 设
是椭圆
上的动点,则
到该椭圆的两个焦点的距离之和为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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3 . 若
三点共线,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431b1672851c36f58e625c5e11bd9f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.3 | B.13 | C.![]() | D.5 |
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4 . 若双曲线
的两条渐近线互相垂直,则两条渐近线方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
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5 . 已知抛物线
和
所围成的封闭曲线
如图所示,点
在曲线
上,给定点
,则下列说法中不正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/940b4bdb-fad3-486f-bc90-fbe59e6f8f3c.png?resizew=162)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7d334f7186c612a2bac12ae5e0365e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6991563453cd366d99513c393d1ccd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/940b4bdb-fad3-486f-bc90-fbe59e6f8f3c.png?resizew=162)
A.任意![]() ![]() ![]() |
B.任意![]() ![]() ![]() |
C.存在![]() ![]() ![]() |
D.任意![]() ![]() ![]() ![]() |
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6 . 如图,
是双曲线
与椭圆
的公共焦点,点
是
在第一象限的公共点,若
,则
的短轴长为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/da775252-8e4b-4a49-9884-a62250edb1e7.png?resizew=177)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9373ed257f417b493c489c8caeabeb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e968a505471270f428d6416a90965f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/da775252-8e4b-4a49-9884-a62250edb1e7.png?resizew=177)
A.1 | B.2 | C.![]() | D.![]() |
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解题方法
7 . 如图,在四棱锥
中,
平面
,底面
为正方形,
.点
在棱
上,过
三点的平面与平面
的交线记为直线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/974e3400-dfcf-44ba-a571-75125ab119ab.png?resizew=147)
(1)求证:
;
(2)若平面
与平面
所成角的余弦值为
.
(i)确定点
的位置;
(ii)求点
到平面
的距离.
![](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/38ae8a383194c8fbb843db7207127a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e8754585a460b01bb92af46cd15b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/974e3400-dfcf-44ba-a571-75125ab119ab.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ee6c7e0dfe134561f818cb51eebe09.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
(i)确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(ii)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
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解题方法
8 . 抛物线
与直线
相交于
两个不同的点.
(1)当
时,求线段
的长;
(2)若
,求直线
的斜率
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd55f837e9c4e6bba1163ef13edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02f266bd253738e315e84231235f0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
9 . 已知
关于直线
的对称点为
,则直线
的方程是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f19b11843421f6082d3aef4115ddd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592a85017ea7dbcc771a1856d5724bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 2020年11月24日中国发射了嫦娥五号采样返回器,并于12月17日在内蒙古自治区四子王族返回地球,带回月壤1731克,标志着我国探月工程“绕、落、回”三步走战略圆满成功,下图是嫦娥五号第一次近月制动后进入了以月球球心为一个焦点的椭圆形轨道(椭圆轨道1),再次制动后降轨变为近圆形环月轨道(椭圆轨道2).若轨道1和轨道2的离心率分别为
,
,则下列判断正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/61c3c178-4c7e-4fe1-b51c-6b3a24b4201a.png?resizew=149)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/61c3c178-4c7e-4fe1-b51c-6b3a24b4201a.png?resizew=149)
A.![]() | B.![]() | C.![]() | D.不能确定 |
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