解题方法
1 . 如图,在四面体
中,
平面
,
.
,
.M是
的中点,P是
的中点,点Q在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/7850d128-eb0e-4c88-bd91-0fe8f8c55fce.png?resizew=190)
(1)证明:
;
(2)若二面角
的大小为60°,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46571701ccaa18d3c844ab99ee6c30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276e3c9755dbd39fb01de614840d230f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/7850d128-eb0e-4c88-bd91-0fe8f8c55fce.png?resizew=190)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be742533a98206940a01156e5cd9ae30.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b70049601f57c8a2ece170c0a9c3c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a72dfbf0138a611174c36ce077e0c47.png)
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2 . 已知椭圆
:
,该椭圆经过点
,且离心率为
.
(1)求椭圆
的标准方程;
(2)设
是圆
上任意一点,由
引椭圆
的两条切线
,
,当两条切线的斜率都存在时,证明:两条切线斜率的积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fcf82d01c39fd2c96e1edba0ad37dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0128793bbbaabe8301b23e4c96ac8583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
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2019-05-19更新
|
3059次组卷
|
4卷引用:山西省永济中学2018-2019学年高二上学期期末考试数学(文)试题
3 . 如图:直三棱柱
中,
为棱
上的一动点,
分别是
,
的重心,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/2ea99702-3a12-4795-b4ea-75d342b3f078.png?resizew=159)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f746310799dace08e9cb13afaf721e2c.png)
(2)若点
在
上的射影正好为
,求
与面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede6a60cad0e0b58e1549fda6e085719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8daddb0812561b9a094aa7e8d8384ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094e639c2b31dc54b1b3e6456e77843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/949dbdab047853e82cbf51ce64d6e3b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d8df438fe1a86803155552db4295c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbcc07eb1ab35de3fb05911220a9cdd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/2ea99702-3a12-4795-b4ea-75d342b3f078.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f746310799dace08e9cb13afaf721e2c.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d8df438fe1a86803155552db4295c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967e9a89e4b6db4bdd7108d5f7af625d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c6ee63b22008f64730404a63967d11.png)
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名校
4 . 如图(1),在等腰梯形
中,
,
是梯形的高,
,
,现将梯形沿
,
折起,使
且
,得一简单组合体
如 图(2)示,已知
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/2017/4/26/1673973295300608/1736580688248832/STEM/2a3358b418994327ab35ddea867012cc.png?resizew=543)
(1)求证:
平面
;
(2)若直线
与平面
所成角的正切值为
,求平面
与平面
所成的锐二面角大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc2cb75b53fea2d000c4e29a65b8301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f36d315245b63a811d5c6f348c17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9366db1b71034abbe1a5693689cf1c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.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/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2017/4/26/1673973295300608/1736580688248832/STEM/2a3358b418994327ab35ddea867012cc.png?resizew=543)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
2017-07-23更新
|
601次组卷
|
3卷引用:【校级联考】山西省芮城县2018-2019学年高二上学期期末考试数学(理)试题
12-13高二上·福建泉州·期末
名校
5 . 已知,椭圆
过点
,两个焦点为
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)
是椭圆
上的两个动点,如果直线
的斜率与
的斜率互为相反数,证明直线
的斜率为定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e90064d012356de1877aa697cd6d6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6917df35ab960d5958af89095219434.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
2016-12-03更新
|
3300次组卷
|
18卷引用:2015-2016学年山西省运城市高二上学期期末理科数学试卷
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6 . 命题:若点O和点F(-2,0)分别是双曲线
(a>0)的中心和左焦点,点P为双曲线右支上的任意一点,则
的取值范围为
.
判断此命题的真假,若为真命题,请做出证明;若为假命题,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d79a9d7c59c061259eba07baded4941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b2bfb98862f33b23a35e24216e6f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87ec6f15899f1752b792cc01ec9802d.png)
判断此命题的真假,若为真命题,请做出证明;若为假命题,请说明理由.
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