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¬å¼ï¼S = b^2*cot(θ/2) ï¼å
¶ä¸ θ å°±æ¯è§ F1PF2 ãè¿å«ç¦ç¹
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ä¸é¢å°±è¯æä¸ï¼ä½ è®°ä½åå°±å¯ä»¥ç¨äºãæ¤åä¸ç±»ä¼¼ï¼æ¯ S = b^2*tan(θ/2) ã
设 |PF1|=mï¼|PF2|=n ï¼
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ä½å¼¦å®çï¼|PF1|^2+|PF2|^2-2|PF1|*|PF2|*cosθ = |F1F2|^2 ï¼
ä¹å³ m^2+n^2-2mncosθ = 4c^2 ï¼------------ï¼1ï¼
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åæ²çº¿å®ä¹ï¼| |PF1|-|PF2| | = 2a ï¼
å¹³æ¹å¾ m^2+n^2-2mn = 4a^2 ï¼-------------ï¼2ï¼
ï¼1ï¼-ï¼2ï¼å¾ 2mn-2mncosθ = 4(c^2-a^2) = 4b^2 ï¼
å æ¤å¯å¾ mn = 2b^2/(1-cosθ)ï¼
æ以ï¼S = 1/2*|PF1|*|PF2|*sinθ = 1/2*mn*sinθ
= b^2*sinθ/(1-cosθ)
= b^2*cot(θ/2) ãè¿éç¨å°
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