1 . 如图,在梯形
中,
,四边形
为矩形,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/ec2aaabc-d685-4966-b7e8-68557c5b3b0b.png?resizew=164)
(1)求证:
;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c66b94f6bc54b0c75063052410cb4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5a68a008a22d5a8cea5fe8dcf31e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/ec2aaabc-d685-4966-b7e8-68557c5b3b0b.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c79c4d655d22f6b3e9826adc6df810.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bfbbf1348a0a35e44cd922afe4cbbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
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名校
2 . 直线
的一个方向向量为
,平面
的一个法向量为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0109eeedaad9fc4bca9050ada0cbf16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97bceae71d4d7e5ed1ec59c8be4bb69.png)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() |
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3 . 如图,空间四边形
中,
,点
为
中点,点
在侧棱
上,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc5343d0ed7b449971c7ba787a621fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d78bc6d40550027a38d2a0518e32fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8926ddd0b69d714c7310cc5bf23d199d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/18/56605350-7615-47cb-8def-b04a990a3641.png?resizew=166)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知双曲线
的右顶点为
, 若以点
为圆心, 以
为半径的圆与双曲线
的一条渐近线交于
两点, 点
为坐标原点, 且
, 则双曲线
的离心率为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec053f40802aa99a5e4c02f2f0b3fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29a5e57dd6a116ac1e2d9711b31b99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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5 . 与椭圆
有相同的焦点,且短半轴长为
的椭圆方程是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540e8cf001345c0ea9b8c1389627357f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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云南省临沧市沧源佤族自治县民族中学2023-2024学年高二上学期期末模拟数学试题上海市松江一中2015-2016学年高二上学期第二次段考(理科)数学试题陕西省咸阳市实验中学2020-2021学年高二上学期第三次月考数学(理)试题广东省鹤山第二中学2020-2021学年高二下学期第一次月考数学试题江苏省镇江市五校2021-2022学年高二下学期3月学情调查考试数学试题(已下线)第13讲 椭圆(2)四川省遂宁中学校2021-2022学年高二下学期期中考试数学(理)试题四川省遂宁中学校2021-2022学年高二下学期期中考试数学(文)试题(已下线)专题3.4 椭圆的简单几何性质-重难点题型检测-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)人教A版(2019) 选修第一册 数学奇书 第三章 学业评价(二十五)人教A版(2019) 选修第一册 数学奇书 第三章 圆锥曲线的方程 3.1 椭圆 3.1.1 椭圆及其标准方程 第1课时 椭圆及其标准方程(一)(已下线)第20讲 椭圆的简单几何性质10种常见考法归类(1)(已下线)3.1.2 椭圆的简单几何性质(10大题型)精讲-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)
解题方法
6 . 已知抛物线
的焦点为
,直线
与
轴的交点为
,与
的交点为
,且
.
(1)当
取得最小值时,求
的值;
(2)当
时,若直线
与抛物线
相交于
两点,与圆
相交于
、
两点,
为坐标原点,
,试问:是否存在实数
,使得
的长为定值?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56e41a284126ca9f8ef0e4549bbb568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaa99a4f236697ba9a9683325c3eb480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0de9020fe30ea581be5b2b243edbbbe.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff657a7566d6a4a5bdefa6227737b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51969fc1a8030cef11cab59267689e89.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/7ac6f581369e7af43ce224589dd4ef10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d700331e1ec034310baa959b9358c257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68aeea8b2ff4169f1a8d9a206e0c31fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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|
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