Question

12£®Èçͼ£¬ÒÑÖªÅ×ÎïÏßy=-x²+bx+c¾­¹ýA£¨0£¬1£©¡¢B£¨4£¬3£©Á½µã£®
£¨1£©ÇóÅ×ÎïÏߵĽâÎöʽ£»
£¨2£©Çótan¡ÏABOµÄÖµ£»
£¨3£©¹ýµãB×÷BC¡ÍxÖᣬ´¹×ãΪC£¬µãMÊÇÅ×ÎïÏßÉϵÄÒ»¸ö¶¯µã£¬Ö±ÏßMNƽÐÐÓÚyÖá½»Ö±ÏßABÓÚN£¬Èç¹ûM¡¢N¡¢B¡¢CΪ¶¥µãµÄËıßÐÎÊÇƽÐÐËıßÐΣ¬ÇëÖ±½Óд³öMµãµÄºá×ø±ê£»
£¨4£©ÒÑÖªµãEΪÅ×ÎïÏßÉÏλÓÚµÚ¶þÏóÏÞÄÚÈÎÒ»µã£¬ÇÒEµãºá×ø±êΪm£¬×÷±ß³¤Îª10µÄÕý·½ÐÎEFGH£¬Ê¹EF¡ÎxÖᣬµãGÔÚµãEµÄÓÒÉÏ·½£¬ÄÇô£¬¶ÔÓÚ´óÓÚ»òµÈÓÚ-1µÄÈÎÒâʵÊým£¬FG±ßÓë¹ýA¡¢BÁ½µãµÄÖ±Ï߶¼Óн»µã£¬Çë˵Ã÷ÀíÓÉ£®

Answer 1

·ÖÎö £¨1£©°ÑA¡¢BÁ½µã×ø±ê´úÈë½âÎöʽ¼´¿É½â¾ö£®
£¨2£©Èçͼ×÷AM¡ÍOB´¹×ãΪM£¬ÀûÓÃtan¡ÏABO=$\frac{AM}{BM}$½â¾ö£®
£¨3£©¸ù¾ÝMN=BC£¬Áгö·½³Ì¼´¿É½â¾ö£®
£¨4£©ÈçͼֻҪÅжÏG_y£¾N_y¼´¿É£®

½â´ð ½â£º£¨1£©ÓÉÌâÒâ$\left\{\begin{array}{l}{c=1}\\{-16+4b+c=3}\end{array}\right.$£¬½âµÃ$\left\{\begin{array}{l}{b=\frac{9}{2}}\\{c=1}\end{array}\right.$£¬ËùÒÔÅ×ÎïÏß½âÎöʽΪy=-x²+$\frac{9}{2}x$+1£®
£¨2£©Èçͼ×÷AM¡ÍOB´¹×ãΪM£¬¡ßÖ±ÏßABµÄ½âÎöʽΪy=$\frac{1}{2}$x+1£¬Ö±ÏßOBµÄ½âÎöʽΪy=$\frac{3}{4}$x£¬
¡àÖ±ÏßAMΪy=-2x+1£¬
ÓÉ$\left\{\begin{array}{l}{y=\frac{3}{4}x}\\{y=-2x+1}\end{array}\right.$½âµÃ$\left\{\begin{array}{l}{x=\frac{4}{11}}\\{y=\frac{3}{11}}\end{array}\right.$£¬
¡àÖ±ÏßµãM×ø±ê£¨$\frac{4}{11}$£¬$\frac{3}{11}$£©
¡àAM=$\frac{4\sqrt{5}}{11}$   BM=$\frac{50}{11}$
¡àtan¡ÏABO=$\frac{AM}{BM}$=$\frac{2\sqrt{5}}{25}$£®
£¨3£©ÉèµãM×ø±êΪ£¨m£¬-m²+$\frac{9}{2}$m+1£©£¬µ±MN¡ÎBC£¬MN=BCʱ£¬M¡¢N¡¢B¡¢CΪ¶¥µãµÄËıßÐÎÊÇƽÐÐËıßÐΣ¬
¡à|-m²+$\frac{9}{2}$m+1-£¨$\frac{1}{2}$m+1£©|=3£¬
ÕûÀíµÃm²-4m+3=0»òm²-4m-3=0£¬
½âµÃm=1»ò3»ò2+$\sqrt{7}$»ò2-$\sqrt{7}$£®
£¨4£©ÈçͼÉèFGÓëÖ±ÏßAB½»ÓÚµãN£¬
¡ßµãEµÄºá×ø±êΪm£¬ÇÒµãEÔÚµÚ¶þÏóÏÞ£¬-1£¼m£¼0£¬
ÓÖ¡ßÕý·½ÐÎEFGHµÄ±ß³¤Îª10£¬
¡àµãFµÄºá×ø±êΪa£¬9£¼a£¼10£¬
¡ßÖ±ÏßABµÄ½âÎöʽΪy=$\frac{1}{2}$x+1£¬
¡àµãNµÄ×Ý×ø±ê$\frac{11}{2}$£¼N_y£¼6£¬
¡ßµãGµÄ×Ý×ø±ê11£¼G_y£¼10£¬
¡àG_y£¾N_y£¬
¡à¶ÔÓÚ´óÓÚ»òµÈÓÚ-1µÄÈÎÒâʵÊým£¬FG±ßÓë¹ýA¡¢BÁ½µãµÄÖ±Ï߶¼Óн»µã£®

µãÆÀ ±¾Ì⿼²é´ý¶¨ÏµÊý·¨È·¶¨¶þ´Îº¯Êý¡¢Ò»´Îº¯Êý½âÎöʽ£¬¿¼²éÈý½Çº¯ÊýµÄ¶¨Ò壬Õý·½ÐεÄÐÔÖʵÈ֪ʶ£¬Ñ§»áÓÃ×Öĸm±íʾÏàÓ¦µÄµãµÄ×ø±êÊǽâ¾öÎÊÌâµÄ¹Ø¼ü£¬ÊÇÊýÐνáºÏµÄÒ»¸öºÃÌâÄ¿£¬ÊôÓÚÖп¼Ñ¹ÖáÌ⣮