名校
解题方法
1 . 已知双曲线
的右焦点为F,c是双曲线C的半焦距,点A是圆
上一点,线段FA与双曲线C的右支交于点B.若
,则双曲线C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7893c7403a17f8ae296fb68fa7bbb92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf571d61abf7a871224de2e4537f37f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f5ead4c208849a901eb56f1d054a21.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-06-08更新
|
856次组卷
|
3卷引用:北京市朝阳区2024届高三下学期质量检测二数学试题
解题方法
2 . 已知
是两个互相垂直的平面,
是两条直线,
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba83980a38c5e1fe4be841bc8a51d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/398fcd2493696aefeb0574d425e67022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90aaadafdc1b5187c6d3a045f44cda91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75350c0f16848247ec0602b0b9a55df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc457ba23645bb1fbaa297c5e565f978.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2024-06-03更新
|
1414次组卷
|
3卷引用:北京市朝阳区2024届高三下学期质量检测二数学试题
解题方法
3 . 已知椭圆E的两个顶点分别为
,
,焦点在x轴上,且椭圆E过点
.
(1)求椭圆E的方程;
(2)设O为原点,不经过椭圆E的顶点的直线l与椭圆E交于两点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0c2c938daac9fd7de1a543fea4d534.png)
,直线BP与直线OC交于点H,点M与点Q关于原点对称.
(i)求点H的坐标(用
,
表示);
(ii)若A,H,M三点共线,求证:直线l经过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108fb116d4b8df0b55280cc50aa378a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6d208692e17b7d9df9886cffee6814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6d973205f1ee6c8ef7a728ed772017.png)
(1)求椭圆E的方程;
(2)设O为原点,不经过椭圆E的顶点的直线l与椭圆E交于两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0c2c938daac9fd7de1a543fea4d534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21e5e78dc87038431fa228f08c16ec4.png)
(i)求点H的坐标(用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
(ii)若A,H,M三点共线,求证:直线l经过定点.
您最近一年使用:0次
解题方法
4 . 已知抛物线
的焦点为F,点P为C上一点.若
,则点 P的横坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd3365c824f7163854320709a382d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f634da4045e2889eef4324d5482b4168.png)
A.5 | B.6 | C.7 | D.8 |
您最近一年使用:0次
5 . 如图,六面体
是直四棱柱
被过点
的平面
所截得到的几何体,
底面
,底面
是边长为2的正方形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2cc24b860b73628561b510910d86484.png)
;
(2)求平面.
与平面
的夹角的余弦值;
(3)在线段 DG上是否存在一点 P,使得
若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c591ef32dbc833e3fabb8e08d62e562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddbb0422a136f45653c8c369f2d75fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2cc24b860b73628561b510910d86484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fb5344a2f52c96039cea0f5a3d5d2e.png)
(2)求平面.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0347559c960fc0c16823caffb4dfb123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)在线段 DG上是否存在一点 P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44171b7935b37c372f4fd4d50c3b72e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e897355151564e9ad86166c7d34424c5.png)
您最近一年使用:0次
解题方法
6 . 已知椭圆
:
的离心率为
,A,B分别是E的左、右顶点,P是E上异于A,B的点,
的面积的最大值为
.
(1)求E的方程;
(2)设O为原点,点N在直线
上,N,P分别在x轴的两侧,且
与
的面积相等.
(i)求证:直线
与直线
的斜率之积为定值;
(ⅱ)是否存在点P使得
,若存在,求出点P的坐标,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求E的方程;
(2)设O为原点,点N在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd5e82b7c5ca802aeac849b41d4928c.png)
(i)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
(ⅱ)是否存在点P使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bfa25b84f0e4b451625efabe1f8f97.png)
您最近一年使用:0次
7 . 如图,在三棱锥
中,侧面
底面
,
,
.
;
(2)已知
,
,
,
是线段
上一点,当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8ff58f671a287701011a1b31e67e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15416b74b2ecbcfa38cf34a9ffff730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06201e4f55b78d8b30afb257d5a1b16b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8ef5efedfdded5f660a01f3b3f7461.png)
您最近一年使用:0次
8 . 已知抛物线
的焦点为
,准线方程为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
__________ ;设
为原点,点
在抛物线上,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd426e7e1e65d91394da0b28d49f65.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c2f156b05838deaae6a35acad242af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b4c1c7fa5884b512da4c8475c07636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bd426e7e1e65d91394da0b28d49f65.png)
您最近一年使用:0次
9 . 已知
,则“
”是“函数
在
上单调递增”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7026803f4884f4de6d964334fc6cafc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
A.充分而不必要条件 | B.必要而不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
解题方法
10 . 在棱长为
的正方体
中,
,
,
分别为棱
,
,
的中点,动点
在平面
内,且
.则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827064e34563a7f678020ee1fa9b1683.png)
A.存在点![]() ![]() ![]() |
B.存在点![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.平面![]() ![]() |
您最近一年使用:0次