å·²ç¥æ¤åCçä¸å¿å¨åæ åç¹ï¼å¯¹ç§°è½´ä¸ºåæ è½´ï¼ç¦ç¹å¨xè½´ä¸ï¼æä¸ä¸ªé¡¶ç¹ä¸ºAï¼-4,0ï¼ï¼ï¼aâ§2ï¼/c=8.ï¼1ï¼æ±æ¤åCçæ¹ç¨ï¼2ï¼è¿Bï¼-1ï¼0ï¼ä½ç´çº¿lä¸æ¤åC交äºEãF两ç¹ï¼çº¿æ®µEFçä¸ç¹ä¸ºMï¼æ±ç´çº¿MAçæçkçåå¼èå´
(1)解æï¼ç±é¢æï¼âµæ¤åä¸é¡¶ç¹A(-4,0)ï¼â´a=4
âµå³ä¾§å线x=a^2/c=8==>c=2==>b^2=a^2-c^2=12
â´æ¤åCçæ¹ç¨:x^2/16+y^2/12=1
(2)解æï¼è®¾è¿ç¹B(-1,0)çç´çº¿ä¸ºy=kx+k==>y^2=k^2x^2+2k^2x+k^2
代å
¥æ¤åå¾(4k^2+3)x^2+8k^2x+4k^2-48=0
设E(x1,y1)ï¼F(x2,y2)
â´x1+x2=-8k^2/(4k^2+3)==>ä¸ç¹M横åæ x0=-4k^2/(4k^2+3)
Y1+y2=k(x1+x2)+2k==>ä¸ç¹M纵åæ y0=k-4k^3/(4k^2+3)
â´AMæç=(y0-0)/(x0+4)=k/[4(k^2+1)]
令f(k)= k/[4(k^2+1)](kâR)
令fâ(k)= (4-4k^2)/[4(k^2+1)]^2=0==>k1=-1,k2=1
f(k)å¨x=-1å¤åæå°å¼-1/8ï¼å¨x=1å¤åæ大å¼1/8
â´ç´çº¿MAçæçkçåå¼èå´ä¸º[-1/8,1/8]
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