题目内容
已知一点P的坐标是(4,-2),直线L的方程是y-x+5=0,曲线C的方程是![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131023212211196009456/SYS201310232122111960094004_ST/0.png)
【答案】分析:曲线C是椭圆,中心在(-1,1),其长轴平行于y轴,短轴平行于x轴.设直线L1过点P(4,-2)且垂直于直线L与曲线C相交于点A、B.L1的方程为y+2=-(x-4),解方程组
,可得到直线L1与曲线C的交点.
解答:解:曲线C是椭圆,中心在(-1,1),
其长轴平行于y轴,短轴平行于x轴
设直线L1过点P(4,-2)且垂直于直线L与曲线C相交于点A、B.
L1的方程为y+2=-(x-4)即y=-x+2.
欲求L1与曲线C的交点,
解方程组![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131023212211196009456/SYS201310232122111960094004_DA/1.png)
得![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131023212211196009456/SYS201310232122111960094004_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131023212211196009456/SYS201310232122111960094004_DA/3.png)
故直线L1与曲线C的交点为A(
,
),B(-1,3).
点评:本题考查椭圆的方程、性质及其应用,解题时要注意公式的灵活运用.
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131023212211196009456/SYS201310232122111960094004_DA/0.png)
解答:解:曲线C是椭圆,中心在(-1,1),
其长轴平行于y轴,短轴平行于x轴
设直线L1过点P(4,-2)且垂直于直线L与曲线C相交于点A、B.
L1的方程为y+2=-(x-4)即y=-x+2.
欲求L1与曲线C的交点,
解方程组
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131023212211196009456/SYS201310232122111960094004_DA/1.png)
得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131023212211196009456/SYS201310232122111960094004_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131023212211196009456/SYS201310232122111960094004_DA/3.png)
故直线L1与曲线C的交点为A(
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131023212211196009456/SYS201310232122111960094004_DA/4.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131023212211196009456/SYS201310232122111960094004_DA/5.png)
点评:本题考查椭圆的方程、性质及其应用,解题时要注意公式的灵活运用.
![](http://thumb2018.1010pic.com/images/loading.gif)
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