名校
1 . 已知函数有两个不同的极值点
,则下列说法不正确的是( )
A.![]() ![]() | B.![]() |
C.当![]() ![]() | D.![]() |
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解题方法
2 . 已知过坐标原点且异于坐标轴的直线交椭圆
于
两点,
为
中点,过
作
轴垂线,垂足为
,直线
交椭圆于另一点
,直线
的斜率分别为
,若
,则椭圆离心率为( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-19更新
|
635次组卷
|
2卷引用:江苏省镇江市2023-2024学年高三下学期期初考试数学试卷
名校
解题方法
3 . 已知结论:椭圆
上一点
处切线方程为
.试用此结论解答下列问题.如图,已知椭圆
:
的右焦点为
,原点为
,椭圆的动弦AB过焦点
且不垂直于坐标轴,弦
的中点为
,椭圆
在点A,B处的两切线的交点为
.
(1)试判断:O,M,N三点是否共线若三点共线,请给出证明;若三点不共线,请说明理由;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a271c22e34d4df61636ab3052a8e0ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1185a977aa9dc61d23db4b658126f8a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa77802f9a072a800ee5098f668d5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/b9703fbb-7e2a-404b-bdfe-c1c16369ef43.png?resizew=161)
(1)试判断:O,M,N三点是否共线若三点共线,请给出证明;若三点不共线,请说明理由;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfba099195b252ab0faba0d8360fae98.png)
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解题方法
4 . “曼哈顿距离”是人脸识别中的一种重要测距方式,其定义如下:设
,
,则
,
两点间的曼哈顿距离
已知
,点
在圆
上运动,若点
满足
,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.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/79c04bbc507d8f917da5253fca7f2c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a5862f87bdbd8d6c653905cddb9900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f6ae1c2a81078eac5ed2f4f823b671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b83e2fc66e8ab0e6f60a1790cea6c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de86d9c0675d246a280f6b71a68aaf9d.png)
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解题方法
5 . 如图,该几何体是由正方形
沿直线
旋转
得到的,已知点
是圆弧
的中点,点
是圆弧
上的动点(含端点),则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12d93bd1130088b622602a6c21c9c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6919ae684f6781571987add69401dbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632049839e056dec120f87fe86fde89e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/f2257834-0640-4408-9615-8e52a8f4446b.png?resizew=161)
A.不存在点![]() ![]() ![]() |
B.存在点![]() ![]() ![]() |
C.存在点![]() ![]() ![]() ![]() |
D.不存在点![]() ![]() ![]() ![]() |
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解题方法
6 . 双曲线
的左、右焦点分别是
,
,离心率为
,点
是
的右支上异于顶点的一点,过
作
的平分线的垂线,垂足是
,
,若
上一点
满足
,则
到
的两条渐近线距离之和为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.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/839c7616cd0d90265f4b2c9c021254fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9659f89dc162060c39417fee994c1bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beed5811999fdba195943b58ab495065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
7 . 已知双曲线
的两条渐近线分别为
上一点
到
的距离之积为
.
(1)求双曲线
的方程;
(2)设双曲线
的左、右两个顶点分别为
为直线
上的动点,且
不在
轴上,直线
与
的另一个交点为
,直线
与
的另一个交点为
,直线
与
轴的交点为
,直线
与
的交点为
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880be90c9e23235e14631dddbb79127d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4b648d890d05c530961ee4670d09eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920124d08222cbe9660c8c3db7a5d31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11449658adfc07dcf4fc0b25e7ed7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e463e661d45282d927b7596d5ad3b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3896bb7e10246b3b8c33da4c500762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee286d0971983740edc17c0e696edb3.png)
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解题方法
8 . 斜率为
的直线
经过双曲线
的左焦点
,与双曲线左,右两支分别交于A,B两点,以双曲线右焦点
为圆心的圆经过A,B,则该双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 如图,在正方体
中,
为棱
上的动点,
为棱
的中点,则下列选项正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/d8383a5f-e75c-4e29-b448-4f64e3f7be3b.png?resizew=160)
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/d8383a5f-e75c-4e29-b448-4f64e3f7be3b.png?resizew=160)
A.直线![]() ![]() |
B.当![]() ![]() ![]() ![]() ![]() |
C.不存在点![]() ![]() ![]() ![]() |
D.三棱锥![]() |
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解题方法
10 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d422c30ef3c8dc03fed384a96832c81d.png)
A.![]() ![]() |
B.![]() ![]() |
C.存在唯一实数![]() ![]() |
D.![]() ![]() |
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