Question

4£®ÔÚÖ±½Ç×ø±êϵxOyÖУ¬Ö±ÏßlµÄ²ÎÊý·½³ÌΪ$\left\{\begin{array}{l}{x=2-\frac{\sqrt{2}}{2}t}\\{y=1+\frac{\sqrt{2}}{2}t}\end{array}\right.$£¨tΪ²ÎÊý£©£®ÔÚ¼«×ø±êÓëÖ±½Ç×ø±êϵxOyÈ¡ÏàͬµÄ³¤¶Èµ¥Î»£¬ÇÒÒÔÔ­µãOΪ¼«µã£¬ÒÔxÖáÕý°ëÖáΪ¼«ÖáµÄ¼«×ø±êϵÖУ¬Ô²CµÄ·½³ÌΪ¦Ñ=4cos¦È£®
£¨¢ñ£© ÇóÔ²CµÄÖ±½Ç×ø±ê·½³Ì£»
£¨¢ò£© ÉèÔ²CÓëÖ±Ïßl½»ÓÚµãA¡¢B£¬ÈôµãPµÄ×ø±êΪ£¨2£¬1£©£¬Çó|PA|+|PB|£®

Answer 1

·ÖÎö £¨1£©ÀûÓÃx=¦Ñcos¦È£¬¦Ñ²=x²+y²£¬½«ÇúÏßCµÄ¼«×ø±ê·½³ÌÊǦÑ=4cos¦È£¬Á½±ßͬ³Ë¦Ñ£¬»¯³ÉÖ±½Ç×ø±ê·½³Ì£»
£¨2£©ÀûÓòÎÊýµÄ¼¸ºÎÒâÒ壬¼´¿ÉÇó|PA|+|PB|£®

½â´ð ½â£º£¨1£©ÇúÏßCµÄ¼«×ø±ê·½³ÌÊǦÑ=4cos¦È£¬ËùÒԦѲ=4¦Ñcos¦È£¬ËüµÄÖ±½Ç×ø±ê·½³ÌÊÇ£ºx²+y²=4x£¬¼´£¨x-2£©²+y²=4¡­£®£¨3·Ö£©
£¨2£©ÉèµãA¡¢B¶ÔÓ¦µÄ²ÎÊý·Ö±ðΪt₁£¬t₂£¬½«$\left\{\begin{array}{l}{x=2-\frac{\sqrt{2}}{2}t}\\{y=1+\frac{\sqrt{2}}{2}t}\end{array}\right.$£¬´úÈ루x-2£©²+y²=4ÕûÀíµÃ${t^2}+\sqrt{2}t-3=0$£¬Ôò$\left\{{\begin{array}{l}{{t_1}+{t_2}=-\sqrt{2}}\\{{t_{1•}}{t_2}=-3}\end{array}}\right.$£¬¡­..£¨5·Ö£©
ÓÖ|PA|+|PB|=$|{t_1}|+|{t_2}|=|{{t_1}-{t_2}}|={£¨{t_1}+{t_2}£©^2}-4{t_1}t{\;}_2=\sqrt{14}$¡­..£¨10·Ö£©

µãÆÀ ±¾Ì⿼²é¼«×ø±ê·½³ÌÓëÖ±½Ç×ø±ê·½³ÌµÄ»¥»¯£¬¿¼²é²ÎÊýÒâÒåµÄÔËÓã¬ÊôÓÚÖеµÌ⣮