某校兴趣小组运用计算机对轮船由海上行驶入内陆海湾进行了一次模拟试验.如图,内陆海湾的入口处有暗礁,图中阴影所示的区域为暗礁区,其中线段
关于坐标轴或原点对称,线段
的方程为
,在海岸和礁石中间的海域可以作为航道通行.有一艘正在海面上航行的轮船准备进入内陆海湾,在点
处测得该船发出的汽笛声的时刻总比在点
测得汽笛声的时刻晚
(设海面上声速为
).若该船沿着当前的航线航行(不考虑轮船的体积)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572664178180096/1572664183857152/STEM/1f1fb26d-6330-4596-aa2f-acac34184ffb.png?resizew=240)
(1)问兴趣小组观察到轮船的当前的航线所在的曲线方程是什么?
(2)这艘船能否由海上安全驶入内陆海湾?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594374a823f13b8958d68f993adf6eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dda248adacad3e8231c69e05bd702a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e42a193359d2fc6c9e1ddc83b24ee3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c99ea60e7ccf33ca5a5e933cc1bc468.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666ac5c50dbe7c30bc8b60d7f7b1b371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3f7b97a269f85cb5009d4a6907d18b.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572664178180096/1572664183857152/STEM/1f1fb26d-6330-4596-aa2f-acac34184ffb.png?resizew=240)
(1)问兴趣小组观察到轮船的当前的航线所在的曲线方程是什么?
(2)这艘船能否由海上安全驶入内陆海湾?请说明理由.
更新时间:2016-12-04 08:16:23
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【推荐1】与圆类似,连接圆锥曲线上两点的线段叫做圆锥曲线的弦,过有心曲线(椭圆,双曲线)中心(即对称中心)的弦叫做有心曲线的直径.对圆
,由直径所对的圆周角是直角出发,可得:若
是圆
的直径,
是圆
上一点(异于
),
均与坐标轴不平行,则
.
(1)试根据点
和直径
的特殊位置,写出椭圆
和双曲线
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(2)对于任意位置满足条件的点
和直径
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3503d330608e7138d1b529aba4512fa.png)
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(1)试根据点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
(2)对于任意位置满足条件的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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【推荐2】设
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
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【推荐1】某团队开发一款“猫捉老鼠”的游戏,如图所示,A、B两个信号源相距10米,O是AB的中点,过O点的直线l与直线AB的夹角为45°,机器猫在直线l上运动,机器鼠的运动轨迹始终满足:接收到A点的信号比接收到B点的信号晚
秒,其中
(单位:米/秒)是信号传播的速度.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/7ee00107-8ccf-44f9-8436-00e91f365180.png?resizew=188)
(1)以O为原点,以OB方向为x轴正方向,且以米为单位建立平面直角坐标系,设机器鼠所在位置为点P,求点P的轨迹方程;
(2)若游戏设定:机器鼠在距离直线l不超过2米的区域运动时,有“被抓”的风险.如果机器鼠保持目前的运动轨迹不变,是否有“被抓”风险?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe04a293e2187f017287312aedc46be6.png)
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(1)以O为原点,以OB方向为x轴正方向,且以米为单位建立平面直角坐标系,设机器鼠所在位置为点P,求点P的轨迹方程;
(2)若游戏设定:机器鼠在距离直线l不超过2米的区域运动时,有“被抓”的风险.如果机器鼠保持目前的运动轨迹不变,是否有“被抓”风险?
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【推荐2】已知
的两个顶点
分别为椭圆
的左焦点和右焦点,且三个内角
满足关系式
.
(1)求线段
的长度;
(2)求顶点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb398137779190b35492d9f06d5fbc3.png)
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【推荐1】如图,由部分椭圆
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的直线
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的方程;
(2)过
的直线
与
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.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/573d0b25ac3ea513b454e803dc9b67a8.png)
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(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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【推荐2】已知曲线C的方程:
,倾斜角为
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,且与曲线C相交于A,B两点.
(1)
时,求三角形
的面积;
(2)在x轴上是否存在定点M,使直线
与曲线C有两个交点A、B的情况下,总有
?如果存在,求出定点M;如果不存在,请说明理由.
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(1)
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(2)在x轴上是否存在定点M,使直线
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