解题方法
1 . 在平面直角坐标系
中,已知双曲线C:
(
,
)的左顶点为
,右焦点为F,过点F作C的一条渐近线的垂线,垂足为P,过点P作x轴的垂线,垂足为Q.若
,
,
成等差数列,则C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a84af713ec9898211637cfa1b0ef3b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56c9f195bc306a5ff74ad29bbd3a6ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c388f1f7160d3397610633dfde015fa0.png)
A.![]() | B.![]() | C.2 | D.![]() |
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名校
2 . 已知O为坐标原点,直线
与抛物线C:
交于A,B两点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15aab800f41f7a47bde139498e19d294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
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2023-02-05更新
|
299次组卷
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2卷引用:江苏省南京市六校联合体2022-2023学年高三下学期1月联考数学试题
3 . 如图在斜三棱柱
中,
,
,
,平面
平面
,E是棱
上一点,D,F分别是AC,AB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/251fd99c-d50e-46b7-bf36-d5aa95fe2a3f.png?resizew=241)
(1)当
,证明:
平面
;
(2)当
,求锐二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4f0c1c9cca0555906d8a53e1a6803d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900e00a3609e6043af1034761d4d65f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4baccc8fc1935fc88f7be136abd058f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/251fd99c-d50e-46b7-bf36-d5aa95fe2a3f.png?resizew=241)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1bfb3449934a7ddb35bde3409d994bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1df970d8b2fcbb38bfac1dc33da9179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926584088b939200d88e64318f2d4e6c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cedf3ce3ac3a1c3f90e88744d940fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6f1d672d4d7775a81ccf0464a8d742.png)
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解题方法
4 . 已知椭圆C:
的左焦点为F,右顶点为
,上、下顶点分别为
,
,线段
的中点E和坐标原点O的连线OE与
垂直,则椭圆C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b93e3f4eb68d7e137c034d9d32094be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc725182c2fd1413319fea35b95c7dc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-02-05更新
|
611次组卷
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2卷引用:江苏省南京市六校联合体2022-2023学年高三下学期1月联考数学试题
解题方法
5 . 已知双曲线E:
的左右焦点分别为
,
.点
为
的中点,O为坐标原点,A,B为双曲线E的左右顶点,P为E上异于A,B的任一点,且满足:直线PA与直线PB的斜率之积为
.
(1)求双曲线E的方程;
(2)过点
作斜率为
的直线l交双曲线E于M,N两点,直线MD,ND分别交双曲线E于P,Q两点,设直线PQ的斜率为k2,问是否存在实数
使得:
?若存在求出
值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](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/0d776a89f4fd29dccffe1040069d59ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d107e77106ff1a9cb76b504bbc99bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)求双曲线E的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252ef4f3003d233ce2467fec89315618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3486e73c205299afe93b217ac848b3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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6 . 已知圆
和定点
P是圆
上任意一点,线段
的垂直平分线交
于点M,设动点M的轨迹为曲线E.
(1)求曲线E的方程;
(2)设
,过
的直线l交曲线E于M,N两点(点M在x轴上方),设直线AM与BN的斜率分别为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efcac5a6477efb54b345aadc1e939a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60a045d16b382314dac977b004be577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
(1)求曲线E的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e44e2b3635b65b4cbea0040b4151ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67351fe10fcfc3f9072eec4c60bfaaa5.png)
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2023-02-04更新
|
695次组卷
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名校
解题方法
7 . 如图,已知正三棱柱ABC-A1B1C1的所有棱长都相等,棱AC,A1C1的中点分别为M,N.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/10/bbf26605-acf0-4e6a-b138-9bbce2825444.png?resizew=162)
(1)求证:B1N⊥C1M;
(2)求异面直线BN与C1M所成角的余弦值;
(3)求平面A1BM与平面ABC1所成二面角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/10/bbf26605-acf0-4e6a-b138-9bbce2825444.png?resizew=162)
(1)求证:B1N⊥C1M;
(2)求异面直线BN与C1M所成角的余弦值;
(3)求平面A1BM与平面ABC1所成二面角的正弦值.
您最近一年使用:0次
2023-02-04更新
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2卷引用:江苏省南京师范大学附属中学江宁分校等2校2022-2023学年高三上学期期末联考数学试题
名校
解题方法
8 . 已知O为坐标原点,点F为抛物线
的焦点,点
,直线
:
交抛物线C于A,B两点(不与P点重合),则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfb23a9e07213cb76990dbedfc7feca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303094682b317daea83be885d1c7ff4b.png)
A.![]() | B.存在实数![]() ![]() |
C.若![]() ![]() | D.若直线PA与PB的倾斜角互补,则![]() |
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9卷引用:江苏省扬州市宝应县2024届高三上学期期末模拟数学试题
9 . 设椭圆
的左焦点为
,右顶点为
.
(1)求椭圆E的方程;
(2)过点
作两条斜率分别为
,
的动直线
,
分别交椭圆于点A、B、C、D,点M、N分别为线段
、
中点,若
,试判断直线
是否经过定点,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b81d7e0ae6cd2a96fa75ede38b5798.png)
(1)求椭圆E的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077855b1492bf35aac52f358e5e093ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f745dbb0d0e93c05041935ea760eb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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10 . 已知非零常数a,若点A的坐标为
,点B的坐标为
,直线
与
相交于点P,且它们的斜率之积为非零常数
,那么下列说法中正确的有( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f01692c28a84e525156d450ea28f5b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf75310b48015af5b03e8b4ea7a16ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.当![]() |
B.当![]() |
C.当![]() |
D.当![]() |
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