1 . 在平面直角坐标系
中,曲线C上的任意一点到点
的距离比到直线
的距离小2.
(1)求曲线C的方程;
(2)过点F作斜率为
的两条直线分别交C于M,N两点和P,Q两点,其中
.设线段
和
的中点分别为A,B,过点F作
,垂足为D.试问:是否存在定点T,使得线段
的长度为定值.若存在,求出点T的坐标及定值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63309dbc3612815f6dbdee23d9a10adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d1bed885fcb17bdcc978ed955677f2b.png)
(1)求曲线C的方程;
(2)过点F作斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25cfd039769976fb02da8a26b8d2957c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33daacca5f6f6681b662295ebb98587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1ab6c10bc0a8bfbdc3b4824c2de1d1.png)
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解题方法
2 . 已知圆
上的动点M在x轴上的投影为N,点C满足
.
(1)求动点C的轨迹方程C;
(2)过点
的直线l与C交于A,B两个不同点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6bdec0f7ba049e55f00b36c4452617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5015c9c4191fd21fa776e5d55572b9cc.png)
(1)求动点C的轨迹方程C;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f449cadb49859b80c31ef1f68bfe81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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2023-02-27更新
|
423次组卷
|
2卷引用:广东省广州市越秀区2022-2023学年高二上学期学业水平调研数学试题
解题方法
3 . 已知曲线
的离心率是
,P为其上顶点,
分别为左、右焦点,过
且垂直于
的直线与C交于
两点,
,则
的周长是_______ .
![](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/4d2a97987f71835f519b462f5b8f5957.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550205cae870d82e19c1e29660bd17b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
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4 . 已知抛物线
的焦点为F,准线为l,过F的直线交C于P、Q两点,交l于点M,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c989e7ad34acf3f50911b01cbe898df.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ac6188f40414f76bc754dee4a75809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cb3d055cd1e7f14afd156a44e2400c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c989e7ad34acf3f50911b01cbe898df.png)
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2023-02-27更新
|
170次组卷
|
2卷引用:广东省广州市越秀区2022-2023学年高二上学期学业水平调研数学试题
解题方法
5 . 已知双曲线
的左,右两焦点分别是
,其中
,直线
与双曲线左支交于A,B两点,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c21b2006b5b4095ac23eca5cbc032e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f5db3e6bd067006556a2f5bedef2ca.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
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解题方法
6 . 在棱长为a的正方体
中,
为底面
内两动点且满足
,异面直线
与
所成角为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0d08fac3054ac8f3b4ef38dc2e0e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab3d7e6077fe7ec725a5637c8bdfee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
A.![]() |
B.直线![]() ![]() |
C.线段![]() ![]() |
D.三棱锥![]() ![]() |
您最近一年使用:0次
2023-02-27更新
|
443次组卷
|
4卷引用:广东省广州市越秀区2022-2023学年高二上学期学业水平调研数学试题
广东省广州市越秀区2022-2023学年高二上学期学业水平调研数学试题江苏省盐城市实验高级中学2022-2023学年高二下学期期中数学试题(已下线)1.2 空间向量基本定理(AB分层训练)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)期末真题必刷压轴60题(23个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
7 . 已知曲线
.( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/543d8305aa5c1a1d523bfb50bf226461.png)
A.若![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若C是等轴双曲线,则以原点为顶点以![]() ![]() |
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解题方法
8 . 已知椭圆
的左、右焦点分别为
,
,过
的直线交椭圆于A,B两点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7315208b83923a2bddaae013f7a6e8.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced7b08dafafb8f1a3cb37b4dd4968e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
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9 . 已知方程
表示椭圆,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c06239ad76993ff9491ab4773471d23.png)
A.m的取值范围为![]() | B.若该椭圆的焦点在y轴上,则![]() |
C.若![]() | D.若![]() ![]() |
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2023-02-25更新
|
904次组卷
|
5卷引用:广东省佛山市顺德区龙江中学、北滘中学等十五校2022-2023学年高二上学期12月月考数学试题
名校
解题方法
10 . 解答下列两个小题:
(1)双曲线
:
离心率为
,且点
在双曲线
上,求
的方程;
(2)椭圆的焦点在
轴上,焦距为
,且经过点
,求椭圆的标准方程.
(1)双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f21c7162941d2b54ebafb1795599195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)椭圆的焦点在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c01be9528bb2c9c9ab3a3296b0c5a3.png)
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