1 . 已知椭圆
的左、右焦点分别为
、
.经过点
且倾斜角为
的直线
与椭圆
交于
、
两点(其中点
在
轴上方),
的周长为8.
(1)求椭圆
的标准方程;
(2)如图,把平面
沿
轴折起来,使
轴正半轴和
轴确定的半平面,与
负半轴和
轴所确定的半平面互相垂直.
,求异面直线
和
所成角的大小;
②若折叠后
的周长为
,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d49bc14700562fee13af6a548e4eaef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5e56b5cbcf69756792fc934bcc20cb.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)如图,把平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
②若折叠后
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5e56b5cbcf69756792fc934bcc20cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7163395f9aaa29be7f6b3106ba48b744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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2 . 如图,
的棱长为1的正方体,任作平面
与对角线
垂直,使得
与正方体的每个面都有公共点,这样得到的截面多边形的面积为
,周长为
的范围分别是_____________ (用集合表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a80427c5520818aa57e4de7bb5ce7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2020/1/12/2375731341819904/2376091990720512/STEM/d9ef730d-97f3-4a80-8db4-452dadf289e8.png)
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3 . 如图所示,将一块直角三角形木板
置于平面直角坐标系中,已知
,点
是三角形木板内一点,现因三角形木板中阴影部分受到损坏,要把损坏部分锯掉,可用经过点
的任一直线
将三角形木板锯成
.设直线
的斜率为
.
![](https://img.xkw.com/dksih/QBM/2017/9/13/1773078348070912/1774098948423680/STEM/503f3c61625043379278d9c666ef7043.png?resizew=172)
(Ⅰ)求点
的坐标及直线
的斜率
的范围;
(Ⅱ)令
的面积为
,试求出
的取值范围;
(Ⅲ)令(Ⅱ)中
的取值范围为集合
,若
对
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc83f34b5a3c1dc09d990ce4bdc8e078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0ebb89b7d83c0a4d1104e0107530d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5f75b19aa58ff52f47217a6882505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://img.xkw.com/dksih/QBM/2017/9/13/1773078348070912/1774098948423680/STEM/503f3c61625043379278d9c666ef7043.png?resizew=172)
(Ⅰ)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(Ⅱ)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(Ⅲ)令(Ⅱ)中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be75fb2da563f2174921ef038acae85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839769901ce89e982e0ae7e836edee1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2017-09-14更新
|
2026次组卷
|
2卷引用:湖北省襄阳市第四中学2017-2018学年高二上学期第一次月考数学试题
4 . 在平面内,
,若动点
满足
,则
的最小值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887edf66180155adb9637b9061922c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffbc423070f5d7ce2c72229066ee1cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd6ba295d535bba546fc9219b7da2b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08012d6e1ae0bfda80a73d3a61531d4a.png)
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5 . 点
为正方体
的内切球
球面上的动点,点
为
上一点,
,若球
的体积为
,则动点
的轨迹的长度为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e731ef1ccc1bded5eb2ea551cd79a12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee3bd4ced831e9000e71ef68c44ac3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2017-05-21更新
|
3677次组卷
|
4卷引用:河北省衡水中学2017届高三下学期第二次摸底考试数学(理)试题
6 . 在平面直角坐标系
中,点T(-8,0),点R,Q分别在
和
轴上,
,点P是线段RQ的中点,点P的轨迹为曲线E.
(1)求曲线E的方程;
(2)直线L与圆
相切,直线L与曲线E交于M,N,线段MN中点为A,曲线E上存在点C满足
(
>0),求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a82b85d3f59cf6c73fd6f31cb8bd097.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/30284bebb9a95ca059d8b3e632bb9713.png)
(1)求曲线E的方程;
(2)直线L与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcb9cbdc9f4bc2c88862bec122a8c635.png)
![](https://img.xkw.com/dksih/QBM/2017/4/14/1665420736135168/1665671461044224/STEM/86cedd0c96f244d7bc75106f9ce8432d.png?resizew=83)
![](https://img.xkw.com/dksih/QBM/2017/4/14/1665420736135168/1665671461044224/STEM/661c86bdbd82424eb927303190f5b3eb.png?resizew=15)
![](https://img.xkw.com/dksih/QBM/2017/4/14/1665420736135168/1665671461044224/STEM/661c86bdbd82424eb927303190f5b3eb.png?resizew=15)
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7 . 当
变化时,不在直线
上的点构成区域G,
是区域G内的任意一点,则
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245a93d9c78da662d75e13f09aed2b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d19081f470baa52d424c4e5259ab0d3.png)
A.(1,2) | B.[![]() ![]() |
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解题方法
8 . 如图,网格纸上小正方形的边长为1,粗实线及粗虚线画出的是某四棱锥的三视图,则该四棱锥各个侧面中,最大的侧面面积为
![](https://img.xkw.com/dksih/QBM/2017/4/10/1662899279675392/1663445712437248/STEM/c8b99258-5c74-436a-9a99-356577961939.png?resizew=207)
![](https://img.xkw.com/dksih/QBM/2017/4/10/1662899279675392/1663445712437248/STEM/c8b99258-5c74-436a-9a99-356577961939.png?resizew=207)
A.2 | B.![]() | C.3 | D.4 |
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解题方法
9 . 把平面图形
上的所有点在一个平面上的射影构成的图形
叫做图形
在这个平面上的射影.如图,在三棱锥
中,
,
,
,
,
,将围成三棱锥的四个三角形的面积从小到大依次记为
,
,
,
,设面积为
的三角形所在的平面为
,则面积为
的三角形在平面
上的射影的面积是
![](https://img.xkw.com/dksih/QBM/2017/3/28/1653753087377408/1656596902756352/STEM/07c1669bb07b4feb900e77cb2c3a00f2.png?resizew=286)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7796caec20ab20a46b31f36a188392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73cab28475a885ff0b5b5d947d65b5ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8739cc8fc1570400f30f5af109a025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a1100f8c8bd07c7dfc3c29991acf00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca201616362528f3615de6edb2317848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56d35b0e69e306a453c5226899c71c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d43eb0b274e00cbbc4a210da4165042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530f5b63e797195906285c0c03eb9276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c2d5971afbff8eca1b9aff5f76f710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e204eeda3cbe67e9e709be5c790b49f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530f5b63e797195906285c0c03eb9276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e204eeda3cbe67e9e709be5c790b49f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/2017/3/28/1653753087377408/1656596902756352/STEM/07c1669bb07b4feb900e77cb2c3a00f2.png?resizew=286)
A.![]() | B.![]() | C.![]() | D.![]() |
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2017-04-01更新
|
1857次组卷
|
6卷引用:2017届四川省成都市高三第二次诊断性检测数学理试卷
2017届四川省成都市高三第二次诊断性检测数学理试卷河北省衡水市衡水中学2019届高三下学期六调考试(文)数学试题(已下线)【全国百强校】河北省衡水中学2019届高三下学期六调考试数学(文)试题四川省泸县第五中学2022-2023学年高三上学期第三学月考试数学(理)试题重庆市万州第二高级中学2023届高三三诊数学试题(已下线)专题8.6 空间直线、平面的垂直(一)【八大题型】-举一反三系列
10 . 正方体
的棱长为a,
分别是棱
的中点,以
为底面作直三棱柱(侧棱与底面垂直的三棱柱叫直三棱柱),若此三棱柱另一底面的三个顶点也都在该正方体的表面上,则这个三棱柱的高为
![](https://img.xkw.com/dksih/QBM/2017/3/20/1647785273647104/1649123888463872/STEM/d26222de-7e01-4c7a-932d-3672c40b3f8c.png?resizew=227)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee56c927039810abe37afcf65e29184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf5bf1816d5dd5da149d1eb164d89ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c089535a04b166290aa4c501cce6bbc.png)
![](https://img.xkw.com/dksih/QBM/2017/3/20/1647785273647104/1649123888463872/STEM/d26222de-7e01-4c7a-932d-3672c40b3f8c.png?resizew=227)
A.![]() | B.![]() |
C.![]() | D.![]() |
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