Question

13£®ÒÑÖª£º·´±ÈÀýº¯Êýy=$\frac{k}{x}$£¨k¡Ù0£©µÄͼÏó¾­¹ýµãB£¨1£¬1£©
£¨1£©Çó¸Ã·´±ÈÀýº¯Êý½âÎöʽ£»
£¨2£©Á¬½ÓOB£¬ÔٰѵãA£¨2£¬0£©ÓëµãBÁ¬½Ó£¬½«¡÷OABÈƵãO°´Ë³Ê±Õë·½ÏòÐýת135¡ãµÃµ½¡÷OA¡äB¡ä£¬Ð´³öA¡äB¡äµÄÖеãPµÄ×ø±ê£¬ÊÔÅжϵãPÊÇ·ñÔÚ´ËË«ÇúÏßÉÏ£¬²¢ËµÃ÷ÀíÓÉ£»
£¨3£©Èçͼ£¬Èô¸Ã·´±ÈÀýº¯ÊýͼÏóÉÏÓÐÒ»µãF£¨2m£¬m-$\frac{1}{2}$£©£¨ÆäÖÐm£¾0£©£¬ÔÚÉäÏßOFÉÏÈÎÈ¡Ò»µãE£¬ÉèEµãµÄ×Ý×ø±êΪn£¬¹ýFµã×÷FM¡ÍxÖáÓÚµãM£¬Á¬½ÓEM£¬Ê¹¡÷OEMµÄÃæ»ýÊÇ$\frac{\sqrt{2}}{2}$£¬ÇónµÄÖµ£®

Answer 1

·ÖÎö £¨1£©°ÑB£¨1£¬1£©´úÈëy=$\frac{k}{x}$¼´¿ÉµÃµ½½áÂÛ£»
£¨2£©¸ù¾ÝÐýתµÄÐÔÖʵõ½¡ÏAOA¡ä=135¡ã£¬OA¡ä=OA£¬¸ù¾ÝÈý½Çº¯ÊýµÄ¶¨ÒåµÃµ½A¡ä£¨-$\sqrt{2}$£¬-$\sqrt{2}$£©£¬B¡ä£¨0£¬-$\sqrt{2}$£©£¬ÓÚÊǵõ½½áÂÛ£»
£¨3£©°ÑF£¨2m£¬m-$\frac{1}{2}$£©´úÈëy=$\frac{1}{x}$£¬µÃµ½m₁=1£¬m₂=-$\frac{1}{2}$£®¸ù¾ÝS_¡÷OEM=$\frac{\sqrt{2}}{2}$£¬ÇóµÃn=$\frac{\sqrt{2}}{2}$£®

½â´ð ½â£º£¨1£©¡ßB£¨1£¬1£©ÔÚy=$\frac{k}{x}$µÄͼÏóÉÏ£¬
¡àk=xy=1¡Á1=1£¬
¡ày=$\frac{1}{x}$£®

£¨2£©Èçͼ1£¬¡ßA£¨2£¬0£©£¬B£¨1£¬1£©£¬
¡àOA=2£¬OB=$\sqrt{2}$£¬
¡ß½«¡÷OABÈƵãO°´Ë³Ê±Õë·½ÏòÐýת135¡ãµÃµ½¡÷OA¡äB¡ä£¬
¡à¡ÏAOA¡ä=135¡ã£¬OA¡ä=OA£¬
¡àA¡ä£¨-$\sqrt{2}$£¬-$\sqrt{2}$£©£¬B¡ä£¨0£¬-$\sqrt{2}$£©£¬
¡àA¡äB¡äµÄÖеãΪP£¨-$\frac{\sqrt{2}}{2}$£¬-$\sqrt{2}$£©£¬
¡ß£¨-$\frac{\sqrt{2}}{2}$£©¡Á£¨-$\sqrt{2}$£©=1£¬
¡àPÔÚË«ÇúÏßÉÏ£»

£¨3£©Èçͼ2£¬¡ßF£¨2m£¬m-$\frac{1}{2}$£©ÔÚ·´±ÈÀýº¯Êýy=$\frac{1}{x}$ͼÏóÉÏ£¬
¡àm₁=1£¬m₂=-$\frac{1}{2}$£®
ÓÖ¡ßm=1£¬
¡àF£¨2£¬$\frac{1}{2}$£©£®
¡ßFM¡ÍxÖᣬ
¡àm£¨2£¬0£©£¬¡àM£¨2£¬0£©£¬¡àOM=2£®
¡ßS_¡÷OEM=$\frac{\sqrt{2}}{2}$£¬
¡à$\frac{1}{2}$OM•n=$\frac{\sqrt{2}}{2}$£¬¼´$\frac{1}{2}$¡Á2n=$\frac{\sqrt{2}}{2}$£¬
¡àn=$\frac{\sqrt{2}}{2}$£®

µãÆÀ ±¾Ì⿼²éÁËÓôý¶¨ÏµÊý·¨Çó·´±ÈÀýº¯ÊýµÄ½âÎöʽ£¬ÐýתµÄÐÔÖÊ£¬Èý½ÇÐÎÃæ»ýµÄ¼ÆË㣬Èñ½ÇÈý½Çº¯Êý£¬µÃ³öA¡ä£¨-$\sqrt{2}$£¬-$\sqrt{2}$£©£¬B¡ä£¨0£¬-$\sqrt{2}$£©ÊǽâÌâµÄ¹Ø¼ü£®