6£®ÉèÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄ×óÓÒ½¹µã·Ö±ðΪF1£¬F2£¬Ï¶¥µãΪB£¬Ö±ÏßBF2µÄ·½³ÌΪx-y-b=0£®
£¨¢ñ£©ÇóÍÖÔ²CµÄÀëÐÄÂÊ£»
£¨¢ò£©ÉèPΪÍÖÔ²ÉÏÒìÓÚÆä¶¥µãµÄÒ»µã£¬Pµ½Ö±ÏßBF2µÄ¾àÀëΪ$\sqrt{2}$b£¬ÇÒÈý½ÇÐÎPF1F2µÄÃæ»ýΪ$\frac{1}{3}$£®
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨2£©ÈôбÂÊΪkµÄÖ±ÏßlÓëÍÖÔ²CÏàÇУ¬¹ý½¹µãF1£¬F2·Ö±ð×÷F1M¡Íl£¬F2M¡Íl£¬´¹×ã·Ö±ðΪM£¬N£¬Çó£¨|F1M|+|F2N|£©•|MN|µÄ×î´óÖµ£®

·ÖÎö £¨¢ñ£©ÓÉÖ±Ïß·½³ÌÇóµÃF2£¨b£¬0£©£¬c=b£¬Ôòa=$\sqrt{2}$c£¬¼´¿ÉÇóµÃÍÖÔ²µÄ±ê×¼·½³Ì£»
£¨¢ò£©£¨1£©ÀûÓõ㵽ֱÏߵľàÀ빫ʽ£¬ÁªÁ¢ÍÖÔ²·½³Ì£¬ÇóµÃPµã×ø±ê£¬ÀûÓÃÈý½ÇÐεÄÃæ»ý¹«Ê½¼´¿ÉÇóµÃbµÄÖµ£¬¼´¿ÉÇóµÃÍÖÔ²·½³Ì£»
£¨2£©·ÖÀàÌÖÂÛ£¬µ±Ö±ÏßбÂÊk¡Ù0ʱ£¬´úÈëÍÖÔ²·½³Ì£¬ÓÉ¡÷-0£¬ÇóµÃmºÍkµÄ¹ØÏµ£¬ÇóµÃ£¨|F1M|+|F2N|£©•|MNØ­£¬ÀûÓûù±¾²»µÈʽµÄÐÔÖʼ´¿ÉÇóµÃ£¨|F1M|+|F2N|£©•|MNحȡֵ·¶Î§£¬µ±k=0£¬ËıßÐÎF1MF2NΪ¾ØÐΣ¬£¨|F1M|+|F2N|£©•|MN|=£¨1+1£©¡Á2=4£¬¼´¿ÉÇóµÃ£¨|F1M|+|F2N|£©•|MN|µÄ×î´óÖµ£®

½â´ð ½â£º£¨¢ñ£©ÓÉÖ±ÏßBF2µÄ·½³ÌΪx-y-b=0£®ÔòF2£¨b£¬0£©£¬c=b£¬
Ôòa2=b2+c2=2c2£¬
ÍÖÔ²µÄÀëÐÄÂÊe=$\frac{c}{a}$=$\frac{\sqrt{2}}{2}$£¬
¡àÍÖÔ²CµÄÀëÐÄÂÊ$\frac{\sqrt{2}}{2}$£»
£¨¢ò£©£¨1£©ÉèP£¨x0£¬y0£©£¬Ôò$\frac{Ø­{x}_{0}-{y}_{0}-bØ­}{\sqrt{2}}$=$\sqrt{2}$b£¬
Ôòx0-y0-3b=0£¬»òx0-y0+b=0£¬
ÓÉ$\left\{\begin{array}{l}{x-y-3b=0}\\{{x}^{2}+2{y}^{2}=2{b}^{2}}\end{array}\right.$£¬Î޽⣬
$\left\{\begin{array}{l}{x-y+b=0}\\{{x}^{2}+2{y}^{2}=2{b}^{2}}\end{array}\right.$£¬½âµÃ£º$\left\{\begin{array}{l}{x=-\frac{4}{3}b}\\{y=-\frac{1}{3}b}\end{array}\right.$£¬
ÓÉ¡÷PF1F2µÄÃæ»ýΪS=$\frac{1}{2}$¡Á2b¡Á$\frac{1}{3}$b=$\frac{1}{3}$£®
½âµÃ£ºb=1£¬
¡àÍÖÔ²µÄ±ê×¼·½³ÌΪ£º$\frac{{x}^{2}}{2}+{y}^{2}=1$£¬
£¨2£©ÉèÖ±Ïßl£ºy=kx+m£¬
Ôò$\left\{\begin{array}{l}{y=kx+m}\\{\frac{{x}^{2}}{2}+{y}^{2}=1}\end{array}\right.$£¬ÕûÀíµÃ£º£¨2k2+1£©x2+4kmx+2m2-2=0£¬
ÓÉ¡÷=£¨4km£©2-4£¨2k2+1£©£¨2m2-2£©=0£¬ÕûÀíµÃm2=2k2+1£¬
Ø­F1MØ­=$\frac{Ø­m-kØ­}{\sqrt{1+{k}^{2}}}$£¬Ø­F2MØ­=$\frac{Ø­m+kØ­}{\sqrt{1+{k}^{2}}}$£¬
µ±k¡Ù0ʱ£¬ÔòØ­MNØ­=$\frac{Ø­{F}_{1}MØ­-Ø­{F}_{2}NØ­}{k}$£¬
Ôò£¨|F1M|+|F2N|£©•|MN|=$\frac{4Ø­kmØ­}{£¨1+{k}^{2}£©Ø­kØ­}$=$\frac{4Ø­mØ­}{£¨1+{k}^{2}£©}$=$\frac{4Ø­mØ­}{1+\frac{{m}^{2}-1}{2}}$=$\frac{8}{Ø­mØ­+\frac{1}{Ø­mØ­}}$¡Ü4£¬
µ±ÇÒ½öµ±Ø­mØ­=1ʱ£¬È¡µÈºÅ£¬
¶øk¡Ù0£¬ÔòØ­mØ­¡Ù1£¬Òò´Ë£¨|F1M|+|F2N|£©•|MN|£¼4£¬
µ±k=0ʱ£¬ËıßÐÎF1MF2NΪ¾ØÐΣ¬
´Ëʱ£¨|F1M|+|F2N|£©•|MN|=£¨1+1£©¡Á2=4£¬
×ÛÉÏ¿ÉÖª£º£¨|F1M|+|F2N|£©•|MN|µÄ×î´óֵΪ4£®

µãÆÀ ±¾Ì⿼²éÍÖÔ²µÄ±ê×¼·½³Ì¼°¼òµ¥¼¸ºÎÐÔÖÊ£¬Ö±ÏßÓëÍÖÔ²µÄλÖùØÏµ£¬¿¼²éÍÖÔ²Óë»ù±¾²»µÈʽµÄ×ÛºÏÀûÓ㬿¼²é·ÖÀàÌÖÂÛ˼Ï룬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

16£®ÕýÈýÀâÖùABC-A1B1C1µ×Ãæ¡÷ABCµÄ±ß³¤Îª3£¬´ËÈýÀâÖùµÄÍâ½ÓÇòµÄ°ë¾¶Îª$\sqrt{7}$£¬ÔòÒìÃæÖ±ÏßAB1ÓëBC1Ëù³É½ÇµÄÓàÏÒֵΪ$\frac{23}{50}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

17£®Öƶ¨Í¶×ʼƻ®Ê±£¬²»½öÒª¿¼ÂÇ¿ÉÄÜ»ñµÃµÄÓ¯Àû£¬¶øÇÒÒª¿¼ÂÇ¿ÉÄܳöÏֵĿ÷Ëð£®Ä³Í¶×ÊÈË´òËãͶ×ʼס¢ÒÒÁ½¸öÏîÄ¿£®¸ù¾ÝÔ¤²â£¬¼×¡¢ÒÒÁ½¸öÏîÄ¿¿ÉÄܵÄ×î´óÓ¯Àû·Ö±ðΪ100%ºÍ50%£¬¿ÉÄܵÄ×î´ó¿÷Ëð·Ö±ðΪ30%ºÍ10%£®Í¶×ÊÈ˼ƻ®Í¶×ʽð¶î²»³¬¹ý10ÍòÔª£¬ÒªÇóÈ·±£¿ÉÄܵÄ×ʽð¿÷Ëð²»³¬¹ý1.8ÍòÔª£®Í¶×ÊÈ˶Լ×ÒÒÁ½¸öÏîÄ¿¸÷Ͷ×ʶàÉÙÍòÔª£¬²ÅÄÜʹ¿ÉÄܵÄÓ¯Àû×î´ó£¿×î´óÓ¯Àû¶îΪ¶àÉÙ£¿

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

14£®ÔĶÁ³ÌÐò¿òͼ£¬ÔËÐÐÏàÓ¦µÄ³ÌÐò£¬ÔòÊä³ösµÄֵΪ£¨¡¡¡¡£©
A£®0B£®2C£®4D£®6

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

1£®ÒÑÖª¶¨ÒåÔÚRÉϵĺ¯Êýf£¨x£©Âú×ãf£¨-x£©=f£¨x£©£¬ÇÒ¶ÔÓÚÈÎÒâx1£¬x2¡Ê[0£¬+¡Þ£©£¬x1¡Ùx2£¬¾ùÓÐ$\frac{f£¨{x}_{2}£©-f£¨{x}_{1}£©}{{x}_{1}-{x}_{2}}$£¾0£¬Èôf£¨-$\frac{1}{3}$£©=$\frac{1}{2}$£¬2f£¨log${\;}_{\frac{1}{8}}$x£©£¼1£¬ÔòxµÄȡֵ·¶Î§Îª£¨0£¬$\frac{1}{2}$£©¡È£¨2£¬+¡Þ£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

11£®ÒÑÖªÅ×ÎïÏߵIJÎÊý·½³ÌΪ$\left\{\begin{array}{l}{x=2p{t}^{2}}\\{y=2pt}\end{array}\right.$£¨tΪ²ÎÊý£©£¬ÆäÖÐp£¾0£¬½¹µãΪF£¬×¼ÏßΪl£¬¹ýÅ×ÎïÏßÉÏÒ»µãM×÷lµÄ´¹Ïߣ¬´¹×ãΪE£¬Èô|EF|=|MF|£¬µãMºá×ø±êΪ6£¬Ôòp=4£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

1£®ÒÑÖªº¯Êýf£¨x£©=$\frac{lnx+a}{x}$-1£¨a¡ÊR£©£®
£¨1£©Èôa=1£¬Çóº¯Êýf£¨x£©µÄ¼«Öµ£»
£¨2£©Èôº¯Êýf£¨x£©ÔÚÇø¼ä£¨0£¬e]ÉÏÓÐÁãµã£¬ÇóʵÊýaµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

18£®$£¨a+\frac{1}{x}£©{£¨1+x£©^4}$Õ¹¿ªÊ½ÖÐx2µÄϵÊýΪ0£¬Ôòa=£¨¡¡¡¡£©
A£®$\frac{2}{3}$B£®$-\frac{2}{3}$C£®$\frac{3}{2}$D£®$-\frac{3}{2}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

19£®ÉèÕýÏîµÈ±ÈÊýÁÐ{an}Ê×Ïîa1=2£¬Ç°nÏîºÍΪSn£¬ÇÒÂú×ã2a3+S2=4£¬ÔòÂú×ã$\frac{66}{65}$£¼$\frac{{S}_{2n}}{{S}_{n}}$£¼$\frac{16}{15}$µÄ×î´óÕýÕûÊýnµÄֵΪ6£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸