名校
1 . 如图,在三棱柱
中,侧面
为矩形.
为
中点,点
在线段
上,且
,求证:
平面
;
(2)若二面角
的大小为
,且
,求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3073cfd9ace3affad3f8ea6824f84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8771e5813d081e1da7acca1ced4947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19129982fd8389238b303e091bd94c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaf581b4f42a25087f7eee23a7d66b6.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfa5b176fd1316fb676bbee21cc5f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74a61581d965458316280968241e4c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13779894af95274a6a3158907dc8bfd6.png)
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2024-04-29更新
|
2127次组卷
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7卷引用:重庆市乌江新高考协作体2023-2024学年高一下学期5月期中数学试题
重庆市乌江新高考协作体2023-2024学年高一下学期5月期中数学试题广东省茂名市高新中学2023-2024学年高一下学期期中测试数学试卷(已下线)第32题 空间角求法迭出,向量法更胜一筹(优质好题一题多解)(已下线)专题3.8 立体中的夹角和距离问题-重难点突破及混淆易错规避(人教A版2019必修第二册)(已下线)6.5.2平面与平面垂直-【帮课堂】(北师大版2019必修第二册)江苏省前黄高级中学2024届高三下学期三模适应性考试数学试题(已下线)2024年新课标全国Ⅰ卷数学真题平行卷(基础)
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2 . 某游乐园中有一座摩天轮.如图所示,摩天轮所在的平面与地面垂直,摩天轮为东西走向.地面上有一条北偏东为
的笔直公路,其中
.摩天轮近似为一个圆,其半径为
,圆心
到地面的距离为
,其最高点为
点正下方的地面
点与公路的距离为
.甲在摩天轮上,乙在公路上.(为了计算方便,甲乙两人的身高、摩天轮的座舱高度和公路宽度忽略不计)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/c50080be-44e3-4828-9bf3-8f8e58a640df.png?resizew=218)
(1)如图所示,甲位于摩天轮的
点处时,从甲看乙的最大俯角的正切值等于多少?
(2)当甲随着摩天轮转动时,从乙看甲的最大仰角的正切值等于多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbbc31960240afea742753b6a8dad6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4053cc2a31e9703bf80b62b5ea18c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c758c27bec97c234d1d818c40f3d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1d5a8cd34aff27b8ed21c977c3946f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d112c9693aa126c92bf1402a1f66bcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/c50080be-44e3-4828-9bf3-8f8e58a640df.png?resizew=218)
(1)如图所示,甲位于摩天轮的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当甲随着摩天轮转动时,从乙看甲的最大仰角的正切值等于多少?
您最近一年使用:0次
2024-02-27更新
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273次组卷
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3卷引用:重庆市乌江新高考协作体2023-2024学年高二下学期开学学业质量联合调研抽测数学试题
名校
解题方法
3 . 设
为实数,直线
和圆
相交于
,
两点.
(1)若
,求
的值;
(2)若点
在以
为直径的圆外(其中
为坐标原点),求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d31d3dffb55d744c8078ab73e1567c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5be29541c139765bfa39c54e15c7a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b93284b0243b7dd327613b1cb42389d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-01-11更新
|
330次组卷
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2卷引用:重庆市乌江新高考协作体2024届高三上学期高考第一次联合调研抽测数学试题
名校
解题方法
4 . 已知圆C与直线
相切于点
,且圆心C在x轴的正半轴上.
(1)求圆C的方程;
(2)过点
作直线交圆C于M,N两点,且M,N两点均不在x轴上,点
,直线BN和直线OM交于点G.证明:点G在一条定直线上,并求此直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276e0fc0eb117d9504dcee30c86650c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedad6bb70631b944c69f8f0b02b35d6.png)
(1)求圆C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316ba5cbb31299d683ac6c7dd795db85.png)
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5 . 已知点
,
,动点
满足
,设动点
的轨迹为曲线
,过曲线
与
轴的负半轴的交点
作两条直线分别交曲线
于点
(异于
),且直线
,
的斜率之积为
.
(1)求曲线
的方程;
(2)证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2699389a501885734a411784cdccf844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7422cbdb4ad06d155abb2ccdb25ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c34edab5c9cdba0b97f74597b5ca85e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2023-11-11更新
|
628次组卷
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2卷引用:重庆市北碚区缙云教育联盟2024届高考零诊数学试题
6 . 已知在平面直角坐标系xOy中,
,
,平面内动点P满足
.
(1)求点P的轨迹方程;
(2)点P轨迹记为曲线C,若曲线C与x轴的交点为M,N两点,Q为直线l:
上的动点,直线MQ,NQ与曲线C的另一个交点分别为E,F,直线EF与x轴交点为K,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ac5904a9ce16e71d2c88a8341bd97b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed40bce11976e6d1a7274116c69c379.png)
(1)求点P的轨迹方程;
(2)点P轨迹记为曲线C,若曲线C与x轴的交点为M,N两点,Q为直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0b49d586e381d72a591858887cca78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe93a54bb5b110827511c70f243871a7.png)
您最近一年使用:0次
7 . 已知圆
,点
,点
为圆
上的动点,线段
的中点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)设
,过点
作与
轴不重合的直线
交曲线
于
两点.
(i)过点
作与直线
垂直的直线
交曲线
于
两点,求四边形
面积的最大值;
(ii)设曲线
与
轴交于
两点,直线
与直线
相交于点
,试讨论点
是否在定直线上,若是,求出该直线方程;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01268ac8e838d0f45ccb35bc1d479d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109a293cef44f23e86e22c1a4cfcbbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a63f7b42555f7f81bcb18b9247bf9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/c1ae536809b1161fd4e83fdc7f42be96.png)
(i)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9ae69e01d76ab5a91ca2b76f8e698e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1522a9c3b2466395570c2689a4055584.png)
(ii)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f5f4ad0caac5a0fecb64f3908d2290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8db072e2b6104671b82f948012fb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2023-10-09更新
|
440次组卷
|
3卷引用:重庆市第七中学校2023-2024学年高二上学期期中考试数学试题
名校
解题方法
8 . 设抛物线
与两坐标轴的交点分别记为M,N,G,曲线C是经过这三点的圆.
(1)求圆C的方程.
(2)过
作直线l与圆C相交于A,B两点,
(i)用坐标法证明:
是定值.
(ii)设
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e6893063df9d4188f3b7002664097d.png)
(1)求圆C的方程.
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cc0f9aa168e43cc5759f017d69b498.png)
(i)用坐标法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559d66fd8b309fd440ce9bda78a579c9.png)
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be14af6ba191f83c422bd408900882b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2397b6e8a1a21509f164d7b4b3382821.png)
您最近一年使用:0次
2023-10-08更新
|
569次组卷
|
3卷引用:重庆市乌江新高考协作体2023-2024学年高二上学期期中学业质量联合调研抽测数学试题
名校
9 . 已知集合:
.
(1)当
取何值时,
为含有两个元素的集合?
(2)当
取何值时,
为含有三个元素的集合?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b055987763c813239f9deca6895ecc9d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b9e10e26024ddc68409dc5bed72179.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b9e10e26024ddc68409dc5bed72179.png)
您最近一年使用:0次
名校
10 . 如图;在三棱柱中;侧面
为矩形.
(1)若
![](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/df5be3cba251ffb7b7959d59aff7dd07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8771e5813d081e1da7acca1ced4947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0230773e811af6aed85f7dc3f6d57fa.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfa5b176fd1316fb676bbee21cc5f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffed75a3a7b15c0eba70e460d326bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10217f7b3ff5ab74c27a0e62debc2ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13779894af95274a6a3158907dc8bfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926d1308d5db144e31b4d0211c63ef52.png)
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