求高手教路!求详细过程!万分感谢!!
a^2=4 ï¼b^2=1 ï¼æ以 c^2=a^2-b^2=3 ï¼
设 Pï¼xï¼yï¼æ¯æ¤åä¸ä»»ä¸ç¹ï¼å·²ç¥ F1ï¼-â3ï¼0ï¼ï¼F2ï¼â3ï¼0ï¼ï¼
æ以 PF1=ï¼-â3-xï¼-yï¼ï¼PF2=ï¼â3-xï¼-yï¼ï¼
å æ¤ PF1*PF2=(-â3-x)(â3-x)+(-y)*(-y)=x^2+y^2-3
=x^2+(1-x^2/4)-3=3/4*x^2-2 ï¼
ç± -2<=x<=2 å¾ 0<=x^2<=4 ï¼
æ以 PF1*PF2 æå°å¼ä¸º -2 ï¼æ大å¼ä¸º 3/4*4-2=1 ã
æ¤é¢å¦ææ¯æ± |PF1|*|PF2| çæå¼ï¼å¯ä»¥éç¨ç¦åå¾å ¬å¼ã
设 Pï¼xï¼yï¼æ¯æ¤åä¸ä»»ä¸ç¹ï¼å |PF1|=a+ex ï¼|PF2|=a-ex ï¼
|PF1|*|PF2|=(a+ex)(a-ex)=a^2-e^2*x^2 ï¼
ç±äº x^2 æå°å¼ä¸º 0 ï¼æ大å¼ä¸º a^2 ï¼
æ以 |PF1|*|PF2| æ大å¼ä¸º a^2=4 ï¼æå°å¼ä¸º a^2-e^2*a^2=b^2=1 ã
设 Pï¼xï¼yï¼æ¯æ¤åä¸ä»»ä¸ç¹ï¼å·²ç¥ F1ï¼-â3ï¼0ï¼ï¼F2ï¼â3ï¼0ï¼ï¼
æ以 PF1=ï¼-â3-xï¼-yï¼ï¼PF2=ï¼â3-xï¼-yï¼ï¼
å æ¤ PF1*PF2=(-â3-x)(â3-x)+(-y)*(-y)=x^2+y^2-3
=x^2+(1-x^2/4)-3=3/4*x^2-2 ï¼
ç± -2<=x<=2 å¾ 0<=x^2<=4 ï¼
æ以 PF1*PF2 æå°å¼ä¸º -2 ï¼æ大å¼ä¸º 3/4*4-2=1 ã
æ¤é¢å¦ææ¯æ± |PF1|*|PF2| çæå¼ï¼å¯ä»¥éç¨ç¦åå¾å ¬å¼ã
设 Pï¼xï¼yï¼æ¯æ¤åä¸ä»»ä¸ç¹ï¼å |PF1|=a+ex ï¼|PF2|=a-ex ï¼
|PF1|*|PF2|=(a+ex)(a-ex)=a^2-e^2*x^2 ï¼
ç±äº x^2 æå°å¼ä¸º 0 ï¼æ大å¼ä¸º a^2 ï¼
æ以 |PF1|*|PF2| æ大å¼ä¸º a^2=4 ï¼æå°å¼ä¸º a^2-e^2*a^2=b^2=1 ã
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