题目内容

(1)椭圆Ca>b>0)与x轴交于AB两点,点P是椭圆C上异于AB的任意一点,直线PAPB分别与y轴交于点MN,求证:为定值

(2)由(1)类比可得如下真命题:双曲线Ca>0,b>0)与x轴交于AB两点,点P是双曲线C上异于AB的任意一点,直线PAPB分别与y轴交于点MN,求证:为定值.请写出这个定值(不要求给出解题过程).

(1)证明:设点

    依题意,得                                                 

   

    令                                                       

    同理得                                                             

   

                                                         

   

                                     

   (2)

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