名校
解题方法
1 . 椭圆
上的任意一点
(除短轴的两个端点外)与短轴的两个端点
的连线分别交
轴于点
和点
,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6205da5e1d2730ee0b3de8bca3e29f5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1fd1784f10d8607df59399dbf5d105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4fd02b843a1cec1fdd6d2beefa98eb.png)
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解题方法
2 . 已知
、
是圆
上的两个不同的动点,且
,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/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab138a74db444886abc7fe18947f7a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dad72fa4f2c1873d938dff7c220370.png)
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2022-12-15更新
|
480次组卷
|
4卷引用:上海市闵行区2023届高三一模数学试题
解题方法
3 . 已知椭圆
为参数,
,
的焦点分别
、
,点
为椭圆
的上顶点,直线
与椭圆
的另一个交点为
.若
,则椭圆
的普通方程为 __ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de38cabb26c37fdeade9988b24b07b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04174f3c9351bc05bcf604d18ab8c44c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4e568d9cd57c442f011a787ab8aaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c2124260496e9307d6448c0c943f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51af88759cdbe6747eaec7ba499b58b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
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解题方法
4 . 已知椭圆
的焦点在
轴上,且以短轴端点和焦点为顶点的四边形是边长为2的正方形.
(1)求椭圆
的标准方程;
(2)若
是椭圆
上的动点,求
的取值范围;
(3)已知不过原点且斜率存在的直线
与椭圆
交异于椭圆顶点的
两点,
为坐标原点,直线
与椭圆
的另一个交点为
点,直线
和直线
的斜率之积为1,直线
与
轴交于点
.若直线
的斜率分别为
,试判断
是否为定值,若是,求出该定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fe9059acc47d2447576e1260c4622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf99adccc80f28343fedd8d0aad7429.png)
(3)已知不过原点且斜率存在的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a8c60eb762b0951c61153fc17ba91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c007b124f9c63a736a265e0e14b7869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42be0cf19dd95496f0ce52f72cd10f44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8394a969dc7b84d0d67ea648c0b4d093.png)
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解题方法
5 . 在平面直角坐标系
中,已知直线l的参数方程为
(t为参数),曲线C的参数方程为
(s为参数).设P为曲线C上的动点,则点P到直线l的距离的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f014c0a4ab67c127debbd9e4ffb63e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a904ef19102c1fad743d6ad99097714.png)
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解题方法
6 . 将参数方程
(
为参数,
)化为普通方程是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93fd64283250178278d400d8145bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
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7 . 关于任意平面向量可实施以下6种变换,包括2种v变换和4种w变换.
:模变为原来的
倍,同时逆时针旋转
;
:模变为原来的
倍,同时顺时针旋转
;
:模变为原来的
倍,同时逆时针旋转
;
:模变为原来的
倍,同时顺时针旋转
;
:模变为原来的
倍,同时逆时针旋转
;
:模变为原来的
倍,同时顺时针旋转
.
记集合
,若每次从集合S中随机抽取一种变换,经过n次抽取,依次将第i次抽取的变换记为
,即可得到一个n维有序变换序列,记为
,则以下判断中正确的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44c235d8b49207ad3f2d77dc5d6cf20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814f55724f7ee57bd395eb3b95393c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3871a062c5e0a4e009b01aa47afb48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a14b56f7f7bb23cd4bf9041e440a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43801f9d9826f8e3646803c915f70e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cde7aace5b888a1a1c26fb911e2f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd028b19c0cbdb7f6f8a6390f7b7fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cde7aace5b888a1a1c26fb911e2f49.png)
记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ef6e24288a68823a7d3143eb547a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bcb95042f427975b9c2f97c109cfae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d0009ab474b946a2abb29803250a1e.png)
A.单位向量![]() ![]() |
B.单位向量![]() ![]() ![]() |
C.若单位向量![]() ![]() ![]() ![]() |
D.单位向量![]() ![]() ![]() |
E.存在n,使得单位向量![]() ![]() ![]() |
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8 . 极坐标方程
化为直角坐标方程为_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09310323ede880374988b4730695fba.png)
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9 . 圆
的参数方程可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . 在极坐标系中,已知点
,
,
是曲线
上任意一点,则
的面积的最小值等于_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86371399e95723ce2ff95c3f921f69fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/befadd728df556c83faba674c103ed83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f7a54779623e137977e29337d8fedb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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