1 . 设双曲线Γ:
,
,B,C在Γ上且直线
经过A.设
分别为Γ在B,C处的切线,点D满足
,则D的轨迹方程是___________ ;若D的横纵坐标均为正整数,且二者之和大于2024,则D可以是_____ .(写出1个即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3674d64026a371b001453280477ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86de0e038b0304e34ca8c9b117fec917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e6aa92080d4e1f43a1ac2f9c2965fe.png)
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解题方法
2 . 在农业生产中,自动化控制技术的应用有效提高了农业生产效率.如图所示,在某矩形试验田
中,
为
中点,
为
中点,三角形
区域种植小麦,梯形
区域种植玉米.为提高劳动效率,节约用水,现采用自动浇水机器人(忽略机器人的面积)对试验田进行灌溉.已知该机器人沿着以
为焦点,
为准线的抛物线运动,且向以自身为圆心,半径为
的圆形区域内浇水.记小麦田能够被机器人灌溉的面积为
,则( )(若直线
与抛物线
相切于点
,平行于
的直线
与
交于
两点,记
与
围成的图形面积为
的面积为
,则
)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/8/c1b1ea7b-130e-42e9-a7a3-db69032da8b3.png?resizew=101)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e453b6640e3dc4c7b7b2a996a2199ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17eefd5373493756cb56389fbec3eca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45cf83ffdd7f12a39d6d2f4c9038cb3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/8/c1b1ea7b-130e-42e9-a7a3-db69032da8b3.png?resizew=101)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 我们称某个曲线族的包络线(Envelope),是跟该曲线族的每条曲线都有至少一点相切的一条曲线.(曲线族即一些曲线的无穷集,它们有一些特定的关系)下列关于包络线的说法正确的是( )
A.设![]() ![]() ![]() ![]() ![]() ![]() 当 ![]() ![]() ![]() |
B.给定正实数![]() ![]() ![]() ![]() ![]() ![]() |
C.设![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.设半径相等的圆![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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