ÌâÄ¿ÄÚÈÝ

11£®Èçͼ£¬ÒÑÖªÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÓÒ×¼ÏßlµÄ·½³ÌΪx=$\frac{4\sqrt{3}}{3}$£¬½¹¾àΪ2$\sqrt{3}$£®
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨2£©¹ý¶¨µãB£¨1£¬0£©×÷Ö±ÏßlÓëÍÖÔ²C½»ÓÚP£¬Q£¨ÒìÓëÍÖÔ²CµÄ×ó¡¢ÓÒ¶¥µãA1£¬A2Á½µã£©£¬ÉèÖ±ÏßPA1ÓëÖ±ÏßQA2ÏཻÓÚµãM£®
¢ÙÈôM£¨4£¬2£©£¬ÊÔÇóµãP£¬QµÄ×ø±ê£»
¢ÚÇóÖ¤£ºµãMʼÖÕÔÚÒ»Ìõ¶¨Ö±ÏßÉÏ£®

·ÖÎö £¨1£©ÓÉÍÖÔ²µÄÀëÐÄÂʹ«Ê½ºÍa£¬b£¬cµÄ¹Øϵ£¬½â·½³Ì¿ÉµÃa£¬b£¬½ø¶øµÃµ½ÍÖÔ²·½³Ì£»
£¨2£©¢ÙÇóµÃÖ±ÏßMA1µÄ·½³ÌºÍÒÔMA2µÄ·½³Ì£¬´úÈëÍÖÔ²·½³Ì£¬ÇóµÃ½»µãP£¬QµÄ×ø±ê£»
¢ÚÉèµãM£¨x0£¬y0£©£¬ÇóµÃÖ±ÏßMA1µÄ·½³ÌºÍÒÔMA2µÄ·½³Ì£¬´úÈëÍÖÔ²·½³Ì£¬ÇóµÃ½»µãP£¬QµÄ×ø±ê£¬½áºÏP£¬Q£¬BÈýµã¹²Ïߣ¬ËùÒÔkPB=kQB£¬»¯¼òÕûÀí£¬¿ÉµÃx0-4=0»ò$\frac{{{x}_{0}}^{2}}{4}$+y02=1£®·Ö±ð¿¼ÂÇ£¬¼´¿ÉµÃµ½µãMʼÖÕÔÚÒ»Ìõ¶¨Ö±Ïßx=4ÉÏ£®

½â´ð ½â£º£¨1£©ÓÉ$\left\{\begin{array}{l}{\frac{{a}^{2}}{c}=\frac{4\sqrt{3}}{3}}\\{2c=2\sqrt{3}}\\{{a}^{2}={b}^{2}+{c}^{2}}\end{array}\right.$£¬µÃ$\left\{\begin{array}{l}{a=2}\\{b=1}\\{c=\sqrt{3}}\end{array}\right.$£¬ËùÒÔÍÖÔ²CµÄ·½³ÌΪ$\frac{{x}^{2}}{4}$+y2=1£®
£¨2£©¢ÙÒòΪA1£¨-2£¬0£©£¬A2£¨2£¬0£©£¬M£¨4£¬2£©£¬
ËùÒÔMA1µÄ·½³ÌΪy=$\frac{1}{3}$£¨x+2£©£¬´úÈëx2+4y2=4£¬
x2-4+4[$\frac{1}{3}$£¨x+2£©]2=0£¬¼´£¨x+2£©[£¨x-2£©+$\frac{4}{9}$£¨x+2£©]=0
ÒòΪA1µÄºá×ø±êΪ-2£¬ËùÒÔxP=$\frac{10}{13}$£¬ÔòyP=$\frac{12}{13}$£¬
ËùÒÔµãPµÄ×ø±êΪ£¨$\frac{10}{13}$£¬$\frac{12}{13}$£©£®
ͬÀí¿ÉµÃµãQµÄ×ø±êΪ£¨$\frac{6}{5}$£¬-$\frac{4}{5}$£©£®
¢ÚÖ¤Ã÷£ºÉèµãM£¨x0£¬y0£©£¬ÓÉÌâÒâxM¡Ù¡À2£®ÒòΪA1£¨-2£¬0£©£¬A2£¨2£¬0£©£¬
ËùÒÔÖ±ÏßMA1µÄ·½³ÌΪy=$\frac{{y}_{0}}{{x}_{0}+2}$£¨x+2£©£¬´úÈëx2+4y2=4£¬
µÃx2-4+4[$\frac{{y}_{0}}{{x}_{0}+2}$£¨x+2£©]2=0£¬¼´£¨x+2£©[£¨x-2£©+$\frac{4{{y}_{0}}^{2}}{£¨{x}_{0}+2£©^{2}}$£¨x+2£©]=0
ÒòΪA1µÄºá×ø±êΪ-2£¬
ËùÒÔxP=$\frac{2-\frac{8{{y}_{0}}^{2}}{£¨{x}_{0}+2£©^{2}}}{1+\frac{4{{y}_{0}}^{2}}{£¨{x}_{0}+2£©^{2}}}$=$\frac{4£¨{x}_{0}+2£©^{2}}{£¨{x}_{0}+2£©^{2}+4{{y}_{0}}^{2}}$-2£¬ÔòyP=$\frac{4£¨{x}_{0}+2£©{y}_{0}}{£¨{x}_{0}+2£©^{2}+4{{y}_{0}}^{2}}$£¬
¹ÊµãPµÄ×ø±êΪ£¨$\frac{4£¨{x}_{0}+2£©^{2}}{£¨{x}_{0}+2£©^{2}+4{{y}_{0}}^{2}}$-2£¬$\frac{4£¨{x}_{0}+2£©{y}_{0}}{£¨{x}_{0}+2£©^{2}+4{{y}_{0}}^{2}}$£©£¬
ͬÀí¿ÉµÃµãQµÄ×ø±êΪ£¨$\frac{-4£¨{x}_{0}-2£©^{2}}{£¨{x}_{0}-2£©^{2}+4{{y}_{0}}^{2}}$+2£¬$\frac{-4£¨{x}_{0}-2£©{y}_{0}}{£¨{x}_{0}-2£©^{2}+4{{y}_{0}}^{2}}$£©
ÒòΪP£¬Q£¬BÈýµã¹²Ïߣ¬ËùÒÔkPB=kQB£¬$\frac{{y}_{P}}{{x}_{P}-1}$=$\frac{{y}_{Q}}{{x}_{Q}-1}$£®
ËùÒÔ$\frac{\frac{4£¨{x}_{0}+2£©{y}_{0}}{£¨{x}_{0}+2£©^{2}+{{y}_{0}}^{2}}}{\frac{4£¨{x}_{0}+2£©^{2}}{£¨{x}_{0}+2£©^{2}+4{{y}_{0}}^{2}}-2-1}$=$\frac{\frac{-4£¨{x}_{0}-2£©{y}_{0}}{£¨{x}_{0}-2£©^{2}+4{{y}_{0}}^{2}}}{\frac{-4£¨{x}_{0}-2£©^{2}}{£¨{x}_{0}-2£©^{2}+4{{y}_{0}}^{2}}+2-1}$£¬¼´$\frac{£¨{x}_{0}+2£©{y}_{0}}{£¨{x}_{0}+2£©^{2}-12{{y}_{0}}^{2}}$=$\frac{-£¨{x}_{0}-2£©{y}_{0}}{-3£¨{x}_{0}-2£©^{2}+4{{y}_{0}}^{2}}$£¬
ÓÉÌâÒ⣬y0¡Ù0£¬ËùÒÔ$\frac{{x}_{0}+2}{£¨{x}_{0}+2£©^{2}-12{{y}_{0}}^{2}}$=$\frac{{x}_{0}-2}{3£¨{x}_{0}-2£©^{2}-4{{y}_{0}}^{2}}$£¬
¼´3£¨x0+2£©£¨x0-2£©2-4£¨x0+2£©y02=£¨x0-2£©£¨x0+2£©2-12£¨x0-2£©y02£¬
ËùÒÔ£¨x0-4£©£¨$\frac{{{x}_{0}}^{2}}{4}$+y02-1£©=0£¬Ôòx0-4=0»ò$\frac{{{x}_{0}}^{2}}{4}$+y02=1£®
Èô$\frac{{{x}_{0}}^{2}}{4}$+y02=1£¬ÔòµãMÔÚÍÖÔ²ÉÏ£¬P£¬Q£¬MΪͬһµã£¬²»ºÏÌâÒ⣮
ËùÒÔxM=4£¬¼´µãMʼÖÕÔÚ¶¨Ö±Ïßx=4ÉÏ£®

µãÆÀ ±¾Ì⿼²éÍÖÔ²µÄ·½³ÌºÍÐÔÖÊ£¬Ö÷Òª¿¼²éÍÖÔ²µÄÀëÐÄÂʺͷ½³ÌµÄÔËÓã¬ÁªÁ¢Ö±Ïß·½³Ì£¬½â·½³ÌÇ󽻵㣬ͬʱ¿¼²éÈýµã¹²ÏßµÄÌõ¼þ£¬¿¼²é»¯¼òÕûÀíµÄÔËËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿

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

¾«Ó¢¼Ò½ÌÍø