题目内容
已知点
满足
,
,
且点P1的坐标是(1,-1)。
(1)求过点P1,P2的直线
的方程;
(2)判断点
与(1)中直线
的位置关系,并用数学归纳法证明你的结论。
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340463621.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340495569.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340635752.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340651663.png)
(1)求过点P1,P2的直线
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340666280.png)
(2)判断点
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340697359.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340666280.png)
(1)
;(2)见解析.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340744620.png)
第一问中,利用
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143408072275.png)
第二问中,猜想点
在直线
上,即
并用数学归纳法给予证明即可。
解:![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143407601536.png)
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143408072275.png)
猜想点
在直线
上,即
.证明如下:
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214341072619.png)
成立。
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143411033604.png)
即
,猜想成立。
即点![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340463621.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214341197482.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143407601536.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143407751647.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143408072275.png)
第二问中,猜想点
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340463621.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340666280.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340916661.png)
解:
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143407601536.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143409471671.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143408072275.png)
猜想点
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340463621.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340666280.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340916661.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214341072619.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214341087615.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232143411033604.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214341134590.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214341150795.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214340463621.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823214341197482.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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