ÌâÄ¿ÄÚÈÝ

2£®ÒÑÖªµãFÊÇÅ×ÎïÏßy2=2pxµÄ½¹µã£¬ÆäÖÐpÊÇÕý³£Êý£¬µãMµÄ×ø±êΪ£¨12£¬8£©£¬µãNÔÚÅ×ÎïÏßÉÏ£¬ÇÒÂú×ã$\overrightarrow{ON}$=$\frac{3}{4}$$\overrightarrow{OM}$£¬OΪ×ø±êÔ­µã£®
£¨1£©ÇóÅ×ÎïÏߵķ½³Ì£»
£¨2£©ÈôAB£¬CD¶¼ÊÇÅ×ÎïÏß¾­¹ýµãFµÄÏÒ£¬ÇÒAB¡ÍCD£¬ABµÄбÂÊΪk£¬ÇÒk£¾0£¬C£®AÁ½µãÔÚxÖáÉÏ·½£¬¡÷AFCÓë¡÷BFDµÄÃæ»ýÖ®ºÍΪS£¬Çóµ±k±ä»¯Ê±SµÄ×îСֵ£®

·ÖÎö £¨1£©ÀûÓÃÒÑÖªÌõ¼þÇó³öp£®¼´¿ÉµÃµ½Å×ÎïÏߵķ½³Ì£®
£¨2£©ÉèÖ±ÏßABµÄ·½³ÌΪy=kx-k£¬A£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬ÁªÁ¢Ö±ÏßÓëÅ×ÎïÏß·½³Ì£¬ÀûÓÃΤ´ï¶¨Àí½áºÏÖ±ÏߵĴ¹Ö±¹Øϵ£¬Çó³öÈý½ÇÐεÄÃæ»ý±í´ïʽ£¬ÀûÓûù±¾²»µÈʽÇó½â¼´¿É£®

½â´ð ½â£º£¨1£©¡ß$\overrightarrow{ON}=\frac{3}{4}\overrightarrow{OM}$£¬¡àN£¨9£¬6£©£¬
ÓеãNÔÚÅ×ÎïÏßÉÏ£¬36=18p£¬
½âµÃp=2£®
ËùÒÔ¸ÃÅ×ÎïÏߵķ½³ÌΪy2=4x£®¡­£¨4·Ö£©
£¨2£©ÓÉÌâÒâµÃÖ±ÏßAB£¬CDµÄбÂʶ¼´æÔÚÇÒ²»ÎªÁ㣬
¡ßF£¨1£¬0£©¡àÉèÖ±ÏßABµÄ·½³ÌΪy=kx-k£¬A£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬
ÓÉ$\left\{\begin{array}{l}{y=kx-k}\\{{y^2}=4x}\end{array}$ÏûÈ¥xµÃ£ºk2x2-£¨2k2+4£©x+k2=0£¬${x_1}+{x_2}=2+\frac{4}{k^2}$£¬x1x2=1£¬¢Ù¡­£¨6·Ö£©
¡ßAB¡ÍCD£¬ÓÃ$-\frac{1}{k}$·´´úÉÏʽÖеÄk£¬Í¬Àí¿ÉµÃ£º${x_3}+{x_4}=2+4{k^2}$£¬x3x4=1¢Ú£»¡­£¨8·Ö£©
${S_{¡÷AFC}}+{S_{¡÷BFD}}=\frac{1}{2}|AF||CF|+\frac{1}{2}|BF||DF|$=$\frac{1}{2}£¨{x_1}+1£©£¨{x_3}+1£©+\frac{1}{2}£¨{x_2}+1£©£¨{x_4}+1£©$=$\frac{1}{2}£¨{x_1}{x_3}+{x_2}{x_4}+{x_1}+{x_2}+{x_3}+{x_4}+2£©$¡­£¨10·Ö£©
½«¢Ù£¬¢Ú´úÈ룬¿ÉµÃ${S_{¡÷AFC}}+{S_{¡÷BFD}}=\frac{1}{2}£¨\frac{1}{{{x_2}{x_4}}}+{x_2}{x_4}+6+\frac{4}{k^2}+4{k^2}£©¡Ý8$£¬£¨µ±ÇÒ½öµ±k=1£¬ÇÒ${x_2}=3-2\sqrt{2}£¬{x_4}=3+2\sqrt{2}$ʱ£¬¡°=¡±³ÉÁ¢£©
¡àS¡÷AFC+S¡÷BFDµÄ×îСֵÊÇ8£®¡­£¨12·Ö£©

µãÆÀ ±¾Ì⿼²éÖ±ÏßÓëÅ×ÎïÏß·½³ÌµÄÓ¦Ó㬻ù±¾²»µÈʽµÄÓ¦Óã¬Å×ÎïÏß·½³ÌµÄÇ󷨣¬¿¼²é¼ÆËãÄÜÁ¦£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿

Î¥·¨ºÍ²»Á¼ÐÅÏ¢¾Ù±¨µç»°£º027-86699610 ¾Ù±¨ÓÊÏ䣺58377363@163.com

¾«Ó¢¼Ò½ÌÍø