解题方法
1 . 已知双曲线
的左、右顶点分别为
,离心率为
.过点
的直线l与C的右支交于M,N两点,设直线
的斜率分别为
.
(1)若
,求
;
(2)证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9c11cc36320090d0aaf0c621a63b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8f7e40ba386c0a9675896b52752d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e4cfa2db814e7e2e8abdf033706420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e607c2f7ae494246768832acb0d54a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3342ecc389773431bc3f64410e41191.png)
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2 . 已知
是圆锥
的底面直径,C是底面圆周上的一点,
,平面
和平面
将圆锥截去部分后的几何体如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/ebb26a22-b021-4be1-82e4-8358117bcf72.png?resizew=153)
(1)证明:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006da854daaec2ed7b17388f640057bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/ebb26a22-b021-4be1-82e4-8358117bcf72.png?resizew=153)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6d39135a2f8472d66ea00eda3b13ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
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3 . 已知椭圆
的左、右焦点分别为F1,F2,设P,Q是E上位于x轴上方的两点,且直线
.若
则E的离心率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a9dc208e4e9a1d015745bba83e45a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0319e91a45d3bd62d6f35a571c3725.png)
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2024-01-26更新
|
583次组卷
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2卷引用:江苏省南通市2024届高三第一次调研测试数学试题
4 . 若向量
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b1aa8b302f5038151b1366a621ef9a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c3566ffa8a7f88642da6e3607efbe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460e5ba67828c57daf2edb497fb52e56.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
解题方法
5 . 已知双曲线C:
(
,
)的两个焦点是
,
,顶点
,点M是双曲线C上一个动点,且
的最小值是
.
(1)求双曲线C的方程;
(2)设点P是y轴上异于C的顶点和坐标原点O的一个定点,直线l过点P且平行于x轴,直线m过点P且与双曲线C交于B,D两点,直线AB,AD分别与直线l交于G,H两点.若O,A,G,H四点共圆,求点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b26461529321c5e669bdf3c489c5d74.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a23e87d16c32b5aa4357f481b5808a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22450bab829ff3a94a6ff713c07adfdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46fd58e40935064129c4676ec310791.png)
(1)求双曲线C的方程;
(2)设点P是y轴上异于C的顶点和坐标原点O的一个定点,直线l过点P且平行于x轴,直线m过点P且与双曲线C交于B,D两点,直线AB,AD分别与直线l交于G,H两点.若O,A,G,H四点共圆,求点P的坐标.
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解题方法
6 . 已知反比例函数
(
)的图象是双曲线,其两条渐近线为x轴和y轴,两条渐近线的夹角为
,将双曲线绕其中心旋转可使其渐近线变为直线
,由此可求得其离心率为
.已知函数
的图象也是双曲线,其两条渐近线为直线
和y轴,则该双曲线的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddcfe70fcf6c4adf6fd7b02911c2cd36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3051f43ac48c0a730a791b8a93ad37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8c576bf76823267df29833499c605d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d532ce76942846df88c6f66112e50f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
7 . 已知抛物线
:
的焦点为
,过点F的直线
与抛物线
交于A,B两点,且直线
的斜率为
,则以线段
为直径的圆的方程为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-01-24更新
|
573次组卷
|
2卷引用:江苏省南京市金陵中学2024届高三上学期期末模拟数学试题
名校
解题方法
8 . 如图所示,四边形ABCD为圆柱ST的轴截面,点Р为圆弧BC上一点(点P异于B,C).
![](https://img.xkw.com/dksih/QBM/2024/1/12/3409766460112896/3409781363875840/STEM/33b6f8354020463fba0be06f8057252b.png?resizew=147)
(1)证明:平面PAB⊥平面PAC;
(2)若
,
(
),且二面角
的余弦值为
,求
的值.
![](https://img.xkw.com/dksih/QBM/2024/1/12/3409766460112896/3409781363875840/STEM/33b6f8354020463fba0be06f8057252b.png?resizew=147)
(1)证明:平面PAB⊥平面PAC;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8798f21caf1819d47db778d23fa57b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2590902f4edd2fa6b233ef54a31862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540ccd15435aa2d59e809d6a28fb2467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d80c787eefc6da2a49d25d2caeaa5fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2024-01-12更新
|
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5卷引用:江苏省苏州市相城区南京师大苏州实验学校2024届高三上学期期末模拟数学试题
名校
解题方法
9 . 在平行六面体
中,底面
为正方形,
,
,侧面
底面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/d599e48f-4857-42ee-b904-a8698642e509.png?resizew=171)
(1)求证:平面
平面
;
(2)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c7761f955e6c49bde5f540a97509b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b5f967c7a8bfdb1dc8c6addcced5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/d599e48f-4857-42ee-b904-a8698642e509.png?resizew=171)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
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2024-01-12更新
|
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名校
解题方法
10 . 已知直线l与椭圆
在第二象限交于
,
两点,
与
轴,
轴分别交于
,
两点(
在椭圆外),若
,则
的倾斜角是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def6b1847098dd39d653c77786cb4eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcbc88687b7cb71577f5622eef66aab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-12更新
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1817次组卷
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