解题方法
1 . 如图,点M为正方形ABCD的中心,N为等边
的边BE的中点,平面
平面ABCD,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/ca2dfb91-6a42-4a10-86c8-058da1a6133d.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/ca2dfb91-6a42-4a10-86c8-058da1a6133d.png?resizew=170)
A.![]() | B.![]() |
C.![]() ![]() | D.![]() ![]() ![]() |
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解题方法
2 . 设双曲线C的中心为坐标原点,渐近线方程为
,且C过点
.
(1)求C的方程;
(2)设不过原点的直线
与C的两支分别交于A,B两点,且
的面积为
.记
,求动点P的轨迹.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3051f43ac48c0a730a791b8a93ad37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937dbb96343b8a9e52718e785e9eda43.png)
(1)求C的方程;
(2)设不过原点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c07068fb03c28403f6c4806ce8af593.png)
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解题方法
3 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de9e2d0a04d2366b868d9dea4bc5359.png)
A.![]() | B.![]() ![]() |
C.![]() ![]() | D.直线![]() ![]() |
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解题方法
4 . 已知数列
满足
,数列
是公差为1的等差数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03328a25e4999b3f2e9afee19b21e94.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70df8a0472e58ff8ba1161b36b15938c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d44b411ed9a1c7795d74d394fb5dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03328a25e4999b3f2e9afee19b21e94.png)
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5 . 在正方体
中,E,F分别为AB,BC的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.![]() ![]() | B.平面![]() ![]() |
C.![]() ![]() | D.平面![]() ![]() |
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解题方法
6 . 已知
,
为椭圆C:
的焦点,过
的直线l与C交A,B两点,则
的内切圆面积最大值为___________ .
![](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/bf6dba18751d6641f9fa02f5756be97a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
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7 . 已知四棱锥
的底面为矩形,
底面
,以
为直径的圆交线段
于点
,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b236510ef2b06323ac4f92157ae3964a.png)
A.![]() ![]() |
B.二面角![]() ![]() |
C.![]() ![]() |
D.存在某个位置![]() ![]() ![]() ![]() |
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8 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12655040661015e5516fd68827c9fc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 如图,在多面体ABCDEF中,四边形CDEF为正方形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/68e49957-818c-4935-93d3-a14074e650cd.png?resizew=174)
(1)设平面
平面
,证明:
;
(2)直线DE上是否存在点G,使得DE⊥平面ABG?若存在,确定G的位置并说明理由;
(3)若
,
,求平面BFG与平面DEA夹角的余弦的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508f6bca26164dbf757f4e2681ea2925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c91baecb97fadd4f8ab49e6effcbc04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343353f850646215dc568fb440fcc0e0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/68e49957-818c-4935-93d3-a14074e650cd.png?resizew=174)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64899adb2cc8913ed7d511eade821422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19fccb51073a0dbb6c7c36c3c375e6d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ffc0e9b3071d12bed38396f05cf5b8.png)
(2)直线DE上是否存在点G,使得DE⊥平面ABG?若存在,确定G的位置并说明理由;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c595984baab06bcab7279f19c5d84aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79296cd4046a71e163a8f3e647a176ae.png)
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解题方法
10 . 已知椭圆C:
(
)的离心率为
,直线l:
是椭圆C与圆
:
的一条公切线.
(1)求椭圆C的方程;
(2)若点
为椭圆C的一点,直线
:
交圆
于M,N两点,以M,N为切点分别作圆
的切线,两条切线交于点Q,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc35409c8054fe18431c70e6fea0334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15839b3af175b63e496dbf320ca7d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
(1)求椭圆C的方程;
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c8d4762cddd87ca1baa79e0d1e158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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