名校
解题方法
1 . 已知
,直线
为平面内的一个动点,过点
作
的垂线,垂足为
,且
,动点
的轨迹记为曲线
.
(1)求
的方程;
(2)若直线
交
于
两点,交圆
于
两点,且
,当
的面积最大时,求
的倾斜角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2f61620e2b2cca65f8e581909658d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd29e35cee24a67a35c043d7b87b654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ad7e0e730caaebab54e28873c38543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
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4卷引用:湖南省娄底市第三中学2023-2024学年高二下学期5月月考数学试题
名校
解题方法
2 . 已知
为坐标原点,若双曲线
的右支上存在两点
,
,使得
,则
的离心率的取值范围是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.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/82e0938b60d9e3f160b5e6b17187056c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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4卷引用:湖南省岳阳市第一中学等多校2023-2024学年高二下学期5月月考数学试题
(已下线)湖南省岳阳市第一中学等多校2023-2024学年高二下学期5月月考数学试题河南省部分重点高中(金科未来)2023-2024学年高二下学期5月大联考数学试题河南省部分重点高中2023-2024学年高二下学期5月质量检测数学试题山西省临汾市部分学校2023-2024学年高二下学期5月质量检测数学试题
名校
3 . 已知函数
,则“
,
”是“
为偶函数”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1009ab48aa7407777999e51a4ba475e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1ff9e9de8658bad54229cb71bd9eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a173784888adf2946382fa093ba53a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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 |
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4卷引用:湖南省长沙市南雅中学2023-2024学年高二下学期第二次月考(5月)数学试题
湖南省长沙市南雅中学2023-2024学年高二下学期第二次月考(5月)数学试题江西省贵溪市实验中学2024届高三下学期5月高考冲刺压轴卷(一)数学试卷(已下线)1.2常见逻辑用语(高三一轮)【同步课时提升卷】(已下线)三角函数-综合测试卷B卷
4 . 已知椭圆
过点
,离心率为
.不过原点的直线
交椭圆
于
两点,记直线
的斜率为
,直线
的斜率为
,且
.
(1)证明:直线
的斜率
为定值;
(2)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a350d44bf2b7ddfbfe23c754efa9c8d4.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
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名校
5 . 如图,在四棱锥
中,
平面
,
,底面
为直角梯形,
,
,
,
是
的中点,点
,
分别在线段
与
上,且
,
.
平面
,求
、
的值;
(2)若
平面
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb466d3d90e7d27f27c60c8beecd4444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9154a06545db6cc85f99a1f8bb95715a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06531ed4a8fc81c1134dbe1e587b19b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b28a07491270be75a3697538bec706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8014e499e7852b587b3b36af14b7816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1afb187132164456d14a203e94cfa385.png)
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名校
解题方法
6 . 如图所示,已知双曲线
的右焦点F,过点F作直线l交双曲线C于
两点,过点F作直线l的垂线交双曲线C于点G,
,且三点
共线(其中O为坐标原点),则双曲线C的离心率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c8091d78595c42d437ff5766431a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26bb3a0cefd6d2c7e136a699d01d1985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f939338ef5c658eecd937afb43d378cd.png)
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名校
解题方法
7 . 在直角坐标系xoy中,动圆M与圆
外切,同时与圆
内切,记圆心M的轨迹为E.
(1)求E的方程;
(2)已知三点T,P,Q在E上,且直线TP与TQ的斜率之积为
;
(i)求证:P,O,Q三点共线;
(ii)若
,直线TQ交x轴于点A,交y轴于点B,求四边形OPAB面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af9ef8ea47d4d912dff5b358d35beae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4405cdec008c6a2e776254cfd4f6c72.png)
(1)求E的方程;
(2)已知三点T,P,Q在E上,且直线TP与TQ的斜率之积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
(i)求证:P,O,Q三点共线;
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f632840491759820c1c5c0a372ad48f5.png)
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解题方法
8 . 已知椭圆
的左、右焦点分别为
为上顶点,离心率 为
,直线
与圆
相切.
(1)求椭圆
的标准方程;
(2)椭圆方程
,平面上有一点
. 定义直线方程
是椭圆
在点
处的极线.
① 若
在椭圆
上,证明: 椭圆
在点
处的极线就是过点
的切线;
② 若过点
分别作椭圆
的两条切线和一条割线,切点为
,割线交椭圆
于
两点,过点
分别作椭圆
的两条切线,且相交于点
. 证明:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d81afe11925b30336768531ede1c278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72dcc2ad9bd83bf683a3c10aebf1c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70993bac22dd8e80a4d151900785a7fb.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)椭圆方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62645f10a184693406c85b90386b43d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f137ff5fe9fd34a482228e24e9a55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74b54fca09a55c3720426e2dc4dfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f137ff5fe9fd34a482228e24e9a55b.png)
① 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f137ff5fe9fd34a482228e24e9a55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
② 若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eebd2e8567f55a4499c51e3c4eed6c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55c23f1782d16f190469765e02b8c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f90c72d708d6d7693d4727ae7882317.png)
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9 . 如图,在四棱台
中,
,
,
.
平面
;
(2)若
,四棱台
的体积为
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feefd792abfb990702d3ef1c8baec6c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c77cb2f11c66a269bbd9d63e4bb6d1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd14966183389b10618cbe33fd777407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901567f610a4e89005799f11e347166e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e5332f18038cc811f7fff449c2d99d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
您最近一年使用:0次
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|
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2卷引用:2024届湖南省长沙市第一中学高考最后一卷数学试题
名校
解题方法
10 . 已知椭圆
的离心率为
,过
的左焦点且斜率为1的直线与
交于
两点.若
,则
的焦距为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58168edb2306922360573f6ba14e90c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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|
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2卷引用:2024届湖南省长沙市第一中学高考最后一卷数学试题