X²/a²+y²/b²=1(aï¼bï¼0)çå·¦å³é¡¶ç¹åå«ä¸ºA.B.ç¹på¨æ¤åä¸ï¼ä¸å¼äºAB两ç¹.O为åæ åç¹.ï¼1ï¼è¥ç´çº¿APä¸BPçæçä¹ç§¯ä¸º-1/2.æ±æ¤åç离å¿ç. ï¼2)è¥AP=OP.è¯æç´çº¿OPçæçâ£Kâ£<â3ã
解ï¼(1)设Pç¹çåæ 为(xï¼y)=(acostï¼bsint)ï¼ç±äºA(-aï¼0)ï¼B(aï¼0)ï¼æ
KAPÃKBP=[bsint/(acost+a)][bsint/(acot-a)]=(b²sin²t)/(a²cos²t-a²)=(b²/a²)[sin²t/(cos²t-1)]
=(b²/a²)[sin²t/(-sin²t)]=-b²/a²=-1/2ï¼æ
b²/a²=(a²-c²)/a²=1-e²=1/2ï¼â´e=â(1/2)=(â2)/2.
(2).è¥AP=OPï¼åæçå¼ï¼(acost+a)²+b²sin²t=a²cos²t+b²sin²tï¼åç®å¾ 2a²cost+a²=0ï¼
æ
cost=-a²/2a²=-1/2ï¼â´tant=-â[(1/cos²t)-1]=-â3ï¼å³æâ£tantâ£=â3ï¼
设OPçå¾è§ä¸ºÎ±ï¼å½På¨ç¬¬äºè±¡éæ¶180°>α>t>90°ï¼(tæ¯æ¤ååæ°è§)ï¼æ
â£KOPâ£=â£tanαâ£<â3ï¼
å½På¨ç¬¬ä¸è±¡éæ¶ï¼tant=â3ï¼180°<α<t<270°ï¼æ
åæ ·æ â£KOPâ£=â£tanαâ£ï¼tanα<â3.
ãåé¢æéï¼ã
温馨提示:答案为网友推荐,仅供参考