8£®ÒÑÖªÍÖÔ²E£º$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1£¨a£¾b£¾0£©$µÄ×ó¡¢ÓÒ½¹µã·Ö±ðΪF1¡¢F2£¬ÀëÐÄÂÊ$e=\frac{{\sqrt{2}}}{2}$£¬PΪÍÖÔ²EÉϵÄÈÎÒâÒ»µã£¨²»º¬³¤Öá¶Ëµã£©£¬ÇÒ¡÷PF1F2Ãæ»ýµÄ×î´óֵΪ1£®
£¨¢ñ£©ÇóÍÖÔ²EµÄ·½³Ì£»
£¨¢ò£©ÒÑÖªÖ±x-y+m=0ÓëÍÖÔ²E½»ÓÚ²»Í¬µÄÁ½µãA£¬B£¬ÇÒÏßABµÄÖе㲻ÔÚÔ²${x^2}+{y^2}=\frac{5}{9}$ÄÚ£¬ÇómµÄȡֵ·¶Î§£®

·ÖÎö £¨¢ñ£©ÓÉÒÑÖªÁйØÓÚa£¬b£¬cµÄ·½³Ì£¬ÁªÁ¢·½³ÌÇóµÃa£¬bµÄÖµ£¬ÔòÍÖÔ²·½³Ì¿ÉÇó£»
£¨¢ò£©ÁªÁ¢Ö±Ïß·½³ÌºÍÍÖÔ²·½³Ì£¬ÀûÓÃÒ»Ôª¶þ´Î·½³ÌµÄ¸ùÓëϵÊýµÄ¹ØÏµÇóµÃABµÄÖеã×ø±ê£¬ÔÙÓÉABµÄÖе㲻ÔÚÔ²${x^2}+{y^2}=\frac{5}{9}$ÄÚ½áºÏÅбðʽ¿ÉµÃmµÄȡֵ·¶Î§£®

½â´ð ½â£º£¨¢ñ£©ÓÉ$e=\frac{{\sqrt{2}}}{2}$£¬µÃ$\frac{c}{a}=\frac{\sqrt{2}}{2}$£¬
ÓÖa2=b2+c2£¬ÇÒ${£¨{s_{¡÷p{F_1}F{\;}_2}}£©_{max}}=\frac{1}{2}¡Á2c¡Áb=1$£¬
ÁªÁ¢½âµÃ£º$a=\sqrt{2}£¬b=1$£¬c=1£®
¡àÍÖÔ²µÄ±ê×¼·½³ÌΪ$\frac{x^2}{2}+{y^2}=1$£»
£¨¢ò£©ÁªÁ¢$\left\{\begin{array}{l}{\frac{{x}^{2}}{2}+{y}^{2}=1}\\{x-y+m=0}\end{array}\right.$£¬ÏûÈ¥yÕûÀíµÃ£º3x2+4mx+2m2-2=0£®
Ôò¡÷=16m2-12£¨2m2-2£©=8£¨-m2+3£©£¾0£¬½âµÃ$-\sqrt{3}£¼m£¼\sqrt{3}$£®
ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬Ôò${x}_{1}+{x}_{2}=-\frac{4m}{3}$£¬
${y}_{1}+{y}_{2}={x}_{1}+{x}_{2}+2m=-\frac{4m}{3}+2m=\frac{2m}{3}$£¬¼´ABµÄÖеãΪ£¨$-\frac{2m}{3}£¬\frac{m}{3}$£©£®
ÓÖABµÄÖе㲻ÔÚÔ²${x^2}+{y^2}=\frac{5}{9}$ÄÚ£¬
¡à$\frac{4{m}^{2}}{9}+\frac{{m}^{2}}{9}=\frac{5{m}^{2}}{9}¡Ý\frac{5}{9}$£¬½âµÃ£ºm¡Ü-1»òm¡Ý1£®
×ÛÉÏ¿ÉÖª£¬$-\sqrt{3}£¼m¡Ü-1$»ò1$¡Üm£¼\sqrt{3}$£®

µãÆÀ ±¾Ì⿼²éÍÖÔ²µÄ¼òµ¥ÐÔÖÊ£¬¿¼²éÁËÖ±ÏßÓëÍÖԲλÖùØÏµµÄÓ¦Óã¬ÊÇÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

18£®ÏÂÁÐ˵·¨ÕýÈ·µÄÊÇ£¨¡¡¡¡£©
A£®¡°f£¨0£©¡±ÊÇ¡°º¯Êý f£¨x£©ÊÇÆæº¯Êý¡±µÄ³äÒªÌõ¼þ
B£®Èô p£º?x0¡ÊR£¬x02-x0-1£¾0£¬Ôò©Vp£º?x¡ÊR£¬x2-x-1£¼0
C£®Èô p¡ÄqΪ¼ÙÃüÌ⣬Ôòp£¬q¾ùΪ¼ÙÃüÌâ
D£®¡°Èô¦Á=$\frac{¦Ð}{6}$£¬Ôòsin¦Á=$\frac{1}{2}$¡±µÄ·ñÃüÌâÊÇ¡°Èô ¦Á¡Ù$\frac{¦Ð}{6}$£¬Ôò sin¦Á¡Ù$\frac{1}{2}$¡±

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®ÒÑÖªa£¾b£¾1£¬Èôlogab+logba=$\frac{10}{3}$£¬ab=ba£¬ÔòÓÉa£¬b£¬3b£¬b2£¬a-2b¹¹³ÉµÄ°üº¬ÔªËØ×î¶àµÄ¼¯ºÏµÄ×Ó¼¯¸öÊýÊÇ£¨¡¡¡¡£©
A£®32B£®16C£®8D£®4

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

16£®ÃüÌâp£ºº¯Êýf£¨x£©=$\left\{\begin{array}{l}{-{x}^{2}+2x£¬x£¼0}\\{ln£¨x+1£©£¬x¡Ý0}\end{array}\right.$ÇÒ|f£¨x£©|¡Ýax£®q£ºº¯Êýg£¨x£©Îª¶¨ÒåÔÚRÉÏµÄÆæº¯Êý£¬µ±x¡Ý0ʱ£¬g£¨x£©=$\frac{1}{2}$£¨|x-a2|+|x-2a2|-3a2£©£¬ÇÒ?x¡ÊR£¬f£¨x-1£©¡Üf£¨x£©ºã³ÉÁ¢£®
£¨1£©ÈôpÇÒqÎªÕæÃüÌ⣬ÇóaµÄȡֵ·¶Î§£»
£¨2£©Èôp»òqÎªÕæÃüÌ⣬ÇóaµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

3£®ÒÔÏÂËĸö¹ØÓÚÔ²×¶ÇúÏßµÄÃüÌâÖУº
¢ÙË«ÇúÏß$\frac{x^2}{16}-\frac{y^2}{9}=1$ÓëÍÖÔ²$\frac{x^2}{49}+\frac{y^2}{24}=1$ÓÐÏàͬµÄ½¹µã£»
¢ÚÒÔÅ×ÎïÏߵĽ¹µãÏÒ£¨¹ý½¹µãµÄÖ±Ïß½ØÅ×ÎïÏßËùµÃµÄÏ߶Σ©ÎªÖ±¾¶µÄÔ²ÓëÅ×ÎïÏßµÄ×¼ÏßÊÇÏàÇеģ»
¢ÛÉèA¡¢BΪÁ½¸ö¶¨µã£¬kΪ³£Êý£¬Èô|PA|-|PB|=k£¬Ôò¶¯µãPµÄ¹ì¼£ÎªË«ÇúÏߣ»
¢Ü¹ý¶¨Ô²CÉÏÒ»µãA×÷Ô²µÄ¶¯ÏÒAB£¬OΪԭµã£¬Èô$\overrightarrow{OP}=\frac{1}{2}£¨\overrightarrow{OA}+\overrightarrow{OB}£©$Ôò¶¯µãPµÄ¹ì¼£ÎªÍÖÔ²£®ÆäÖÐÕýÈ·µÄ¸öÊýÊÇ£¨¡¡¡¡£©
A£®1¸öB£®2¸öC£®3¸öD£®4¸ö

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

13£®É躯Êýf£¨x£©=$\left\{\begin{array}{l}{{x}^{2}+bx+2£¬x¡Ü0}\\{|2-x|£¬x£¾0}\end{array}\right.$£¬Èôf£¨-4£©=f£¨0£©£¬Ôòº¯Êýy=f£¨x£©-ln£¨x+2£©µÄÁãµã¸öÊýÓУ¨¡¡¡¡£©
A£®6B£®4C£®5D£®7

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

20£®ÉèµÈ²îÊýÁÐ{an}µÄǰnÏîºÍΪSn£¬ÈôSk=2£¬S3k=18£¬ÔòS4k=£¨¡¡¡¡£©
A£®24B£®28C£®32D£®54

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

17£®Ö´ÐÐÈçͼËùʾµÄÁ÷³Ìͼ£¬ÔòÊä³öµÄMӦΪ2 

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

18£®ÒÑÖªÍÖÔ²C£º$\frac{x^2}{a^2}+\frac{y^2}{b^2}$=1£¨a£¾b£¾0£©µÄÓÒ½¹µãΪF£¬¹ýµãFµÄÖ±Ïß½»yÖáÓÚµãN£¬½»ÍÖÔ²CÓÚµãA¡¢P£¨PÔÚµÚÒ»ÏóÏÞ£©£¬¹ýµãP×÷yÖáµÄ´¹Ïß½»ÍÖÔ²CÓÚÁíÍâÒ»µãQ£®Èô$\overrightarrow{NF}=2\overrightarrow{FP}$£®
£¨1£©ÉèÖ±ÏßPF¡¢QFµÄбÂÊ·Ö±ðΪk¡¢k'£¬ÇóÖ¤£º$\frac{k}{k'}$Ϊ¶¨Öµ£»
£¨2£©Èô$\overrightarrow{AN}=\overrightarrow{FP}$ÇÒ¡÷APQµÄÃæ»ýΪ$\frac{{12\sqrt{15}}}{5}$£¬ÇóÍÖÔ²CµÄ·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸