题干

已知点F(1,0),点A是直线l1:x=﹣1上的动点,过A作直线l2,l1⊥l2,线段AF的垂直平分线与l2交于点P.

(Ⅰ)求点P的轨迹C的方程;

(Ⅱ)若点M,N是直线l1上两个不同的点,且△PMN的内切圆方程为x2+y2=1,直线PF的斜率为k,求

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K
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M
N
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的取值范围.
上一题 下一题 0.0难度 选择题 更新时间:2013-01-14 05:46:32

答案(点此获取答案解析)

解:(Ⅰ)∵点F(1,0),点A是直线l1:x=﹣1上的动点,过A作直线l2,l1⊥l2,线段AF的垂直平分线与l2交于点P,

∴点P到点F(1,0)的距离等于它到直线l1的距离,

∴点P的轨迹是以点F为焦点,直线l1:x=﹣1为准线的抛物线,

∴曲线C的方程为y2=4x.

(Ⅱ)设P(x

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阅读理解

    A new phone app uses shaking from smartphones to warn people about earthquakes. The new app is called MyShake, which is the work of four researchers at the University of California. Berkeley.

    Smartphones are equipped with accelerometers(加速器). MyShake uses phone accelerometers to measure seismic (地震的) activity. It has been programmed to know the difference between normal activity and earthquake movement. The software developers say their app is right 93 percent of the time. A smartphone sends seismic information to the app developers. If the developers receive several warnings from one area, it recognizes that an earthquake may be taking place or will take place soon. Using information sent from the app, the network then judges the location and strength of the quake in real time. MyShake can record 5.0 earthquake at distances of 10 kilometers or less.

    MyShake uses very little power, according to its developers. Only when seismic activity is sensed by the app does it become active and sends data to the network. The app works best when your phone is resting on a flat surface, like a table.

    The developers hope that MyShake can add to information collected by the U.S Geological Survey. That U.S agency has created the Earthquake Early Warning System, also known as the EEW. The EEW has used sensors for measuring quakes in many areas. In places where no such equipment exists, MyShake may be the only method of early quake detection (发现). The app also shows ways to stay safer during an earthquake. The developers say it will become more effective as more people use it.

    The developers say they hope to add a feature that will warn people about possible tsunami after an earthquake.

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