解题方法
1 . 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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2 . 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
3 . 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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4 . 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
5 . 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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解题方法
6 . 若抛物线
上的动点M到其焦点F的距离的最小值为1,则p的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
A.1 | B.![]() | C.2 | D.4 |
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7 . 设F为抛物线C:
的焦点,A为平面内定点,若抛物线C上存在点P使得
的最小值为5,则点A可以为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088fcdd595455906a1a7080d630611f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44331dd46961efa418e3261d4014b2f7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 已知
为椭圆
的两个焦点,过
的直线与C交于M,N两点.若
,
,则C的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b7b8327139b0058a512a8b256f1a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7155f4135d1d728947cb3986675533.png)
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9 . 如图,在三棱柱
中,D为
的中点,
,平面
平面
.
平面
;
(2)设
,四棱锥
的体积为
,求平面
与平面ABC所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac96a75b3a3a7b0a36bb1f0d04563e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ba609142a263c93c2b81fafc6d2034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a721c8a8da776f6dbe349e3f98e7a878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0b89497679f4adce65b610e49d6159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca6a9d7a5eaa4e5d39aa1544f95342.png)
您最近一年使用:0次
2024-02-04更新
|
463次组卷
|
5卷引用:江西省赣州市2024届高三上学期期末数学试题
江西省赣州市2024届高三上学期期末数学试题江西省宜春市丰城市第九中学2023-2024学年高二下学期开学考试数学试题湖南省株洲市第一中学2022届高三上学期期中数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 立体几何非常规建系问题 微点1 立体几何非常规建系问题(一)【培优版】广东省广州市三中2023-2024学年高二下学期期中数学试题
解题方法
10 . 已知
,
为双曲线C:
(
,
)的两个焦点,以
为直径的圆与C在第一象限的交点为P,若
,则C的离心率为( )
![](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/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29aa3bd463abf39a3f63e077abcc28.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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