名校
1 . 若给定椭圆
和点
,则称直线
为椭圆C的“伴随直线”.
(1)若
在椭圆C上,判断椭圆C与它的“伴随直线”的位置关系(当直线与椭圆的交点个数为0个、1个、2个时,分别称直线与椭圆相离、相切、相交),并说明理由;
(2)命题:“若点
在椭圆C的外部,则直线
与椭圆C必相交.”写出这个命题的逆命题,判断此逆命题的真假,说明理由;
(3)若
在椭圆C的内部,过N点任意作一条直线,交椭圆C于A、B,交
于M点(异于A、B),设
,问
是否为定值?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c0e3eaf99511bb61410a1a0d10cd26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8e91ef21035cdf41befe47fc3bc728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad019278b09c3bac2883ccc674cdf4ba.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8e91ef21035cdf41befe47fc3bc728.png)
(2)命题:“若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8e91ef21035cdf41befe47fc3bc728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8e91ef21035cdf41befe47fc3bc728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1616837b5387600bc74b2e2e02b62a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
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