名校
1 . 如图,在三棱柱
中,侧面
为矩形,侧面
底面
,
为等边三角形,
,
,点
在
上,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/24a32855-bc47-44f0-9db2-98b69b1d0b47.png?resizew=151)
(1)求证:
为
中点;
(2)设
上一点
,若平面
与平面
的夹角的余弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9bdbbdfabc737323692c796e41930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d97f616f0f32beed421129cbbb4db8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ed3f684e1cd7d210d6646ab1155ce5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/24a32855-bc47-44f0-9db2-98b69b1d0b47.png?resizew=151)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)设
![](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/f284572d7511101af0077ab2a1c68715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a527c6707a945f96216368232f9d9a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453e04c6bf888987cd1a150a65898a59.png)
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2024-02-20更新
|
537次组卷
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2卷引用:北京市平谷区2023-2024学年高二上学期期末教学质量监控数学试卷
23-24高二上·北京·期末
名校
2 . 在平面直角坐标系中画出方程
表示的曲线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23d97f6bef4032d435ca2c5a09d89d2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/59691968-2b31-4346-b1f2-948c849ad3db.png?resizew=241)
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23-24高二上·北京·期末
名校
3 . 如图所示的圆锥中,高
,底面的直径
.M为母线PB的中点.若平面
经过OM且垂直于轴截面PAB,根据圆锥曲线的定义,可以证明此时平面
与圆锥侧面的交线为抛物线的一部分,则下面四个结论中错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/91997093-bae0-4fdf-875a-52cfa23b661b.png?resizew=149)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0819cd060cdfb72896f379db29a4724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/91997093-bae0-4fdf-875a-52cfa23b661b.png?resizew=149)
A.M为抛物线的顶点 | B.直线OM为抛物线的对称轴 |
C.O是抛物线的焦点 | D.抛物线的焦点到准线的距离为![]() |
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名校
4 . 如图,四边形
为矩形,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/2291c52c-333b-4e2a-9b4d-f4935ce88a93.png?resizew=151)
(1)求证:
平面
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/691dbdfcf0dfc86e8892eb9ff4edb764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde10d68d53e859e524ae9cfb9ce76c8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/2291c52c-333b-4e2a-9b4d-f4935ce88a93.png?resizew=151)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
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270次组卷
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2卷引用:北京市清华附中高22级2023-2024学年高二上学期期末数学试题
名校
解题方法
5 . 已知椭圆
的焦距为
,下顶点
和右顶点
的距离为
,
(1)求椭圆
方程;
(2)设不经过右顶点的直线
交椭圆
于两点
,过点
作
轴的垂线交直线
于点
,交直线
于
,若点
为线段
的中点,求证:直线
经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.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/d4056761b8f826eeb6ad8c9a151d3c9c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设不经过右顶点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-02-18更新
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316次组卷
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2卷引用:北京市清华附中高22级2023-2024学年高二上学期期末数学试题
名校
解题方法
6 . 已知点F是双曲线
的一个焦点,直线
,则“点F到直线l的距离大于1”是“直线l与双曲线C没有公共点”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4058fc45c49e6710ba7e273cb7888704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3016baf1a9ce777f16ea9ce469b2510.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充分必要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2024-02-18更新
|
188次组卷
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2卷引用:北京市清华附中高22级2023-2024学年高二上学期期末数学试题
解题方法
7 . 已知椭圆
的左右焦点分别为
,
,设椭圆
上一点
(不与左右顶点重合),直线
与椭圆的另一个交点为
,且
的周长为6.
(1)求椭圆
的标准方程;
(2)已知点
为椭圆的左顶点,直线
,
分别与直线
交于
,
两点.试判断:以
为直径的圆与直线
的位置关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a77552a1b379918add59e05fa6efab5.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/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4085b194990fc17f8073878b8eca1a29.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
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8 . 已知椭圆
的两个焦点分别为
,
,若点
在椭圆上,且
,则点
到
轴的距离为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f9bdc6d9f09e14b037ea7d3ee1f623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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9 . 如图,已知M是抛物线C:
(
)上一点,F是抛物线C的焦点,以Fx为始边,FM为终边的
,且
,l为抛物线C的准线,O为原点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ef229c07-5c27-49d4-9561-83b588dc021a.png?resizew=141)
(1)求抛物线C的方程;
(2)若直线FM与抛物线C交于另一个点N,过N作x轴的平行线与l相交于点E.求证:M,O,E三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bac87db382874f77ec5720a8023f9dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d55a119f97c226cbd2fc6419e4ed19c0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/ef229c07-5c27-49d4-9561-83b588dc021a.png?resizew=141)
(1)求抛物线C的方程;
(2)若直线FM与抛物线C交于另一个点N,过N作x轴的平行线与l相交于点E.求证:M,O,E三点共线.
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解题方法
10 . 过双曲线
的右焦点
引圆
的切线,切点为
,延长
交双曲线
的左支于点
.若
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4be819fc47b2aa19ab2022b3dfeb6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c2293f93791a597bf0162411f3395f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7947b4868f6efbdadcee2e1baab0be9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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