6£®ÒÑÖªÔ²C£ºx2+y2-x-y=0¾­¹ýÍÖÔ²E£º$\frac{x^2}{a^2}$+$\frac{y^2}{b^2}$=1£¨a£¾b£¾0£©µÄÓÒ½¹µãFºÍÉ϶¥µãD£®
£¨¢ñ£©ÇóÍÖÔ²EµÄ·½³Ì£»
£¨¢ò£©¹ýµãP£¨-2£¬0£©×÷бÂʲ»ÎªÁãµÄÖ±ÏßlÓëÍÖÔ²E½»ÓÚ²»Í¬µÄÁ½µãA£¬B£¬Ö±ÏßAF£¬BF·Ö±ð½»ÍÖÔ²EÓÚµãG£¬H£¬Éè$\overrightarrow{AF}$=¦Ë1$\overrightarrow{FG}$£¬$\overrightarrow{BF}$=¦Ë2$\overrightarrow{FH}$£®£¨¦Ë1£¬¦Ë2¡ÊR£©
£¨i£©Çó¦Ë1+¦Ë2µÄȡֵ·¶Î§£»
£¨ii£©ÊÇ·ñ´æÔÚÖ±Ïßl£¬Ê¹µÃ|AF|•|GF|=|BF|•|HF|³ÉÁ¢£¿Èô´æÔÚ£¬ÇólµÄ·½³Ì£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

·ÖÎö £¨¢ñ£©ÔÚÔ²C£ºx2+y2-x-y=0ÖУ¬Áîy=0£¬µÃF£¨1£¬0£©£¬ÇóµÃc£¬½â³öÍÖÔ²·½³Ì£®
£¨¢ò£©£¨i£©ÉèÖ±ÏßµÄбÂÊΪk£¬A£¨x1£¬y1£©B£¨x2£¬y2£©£¬G£¨x3£¬y3£©£¬H£¨x4£¬y4£©£¬¸ù¾ÝÌõ¼þÁгö¹ØÓÚyµÄÒ»Ôª¶þ´Î·½³Ì£¬ÔÙÉèÉèÖ±ÏßlµÄ·½³ÌΪy=k£¨x+2£©£¬´úÈë$\frac{{x}^{2}}{2}+{y}^{2}=1$£¬µÃʽÇó½â¼´¿É£®
£¨ii£©|AF|=¦Ë1|FG|£¬|BF|=¦Ë2|FH|¼´|FG|=$\frac{|AF|}{{¦Ë}_{1}}£¬|FH|=\frac{|BF|}{{¦Ë}_{2}}$£¬´úÈë|AF||GF|=|BF||HF|µÃ|AF|2£¬|BF|2»¯¼òÕûÀí¼´¿É£®

½â´ð ½â£º£¨¢ñ£©ÔÚÔ²C£ºx2+y2-x-y=0ÖУ¬Áîy=0£¬µÃF£¨1£¬0£©£¬¼´c=1
Áîx=0£¬µÃD£¨0£¬1£©£¬¼´b=1
ËùÒÔa2=b2+c2=2
¼´ÍÖÔ²µÄ·½³ÌΪ$\frac{{x}^{2}}{2}+{y}^{2}=1$
£¨¢ò£©£¨i£©ÉèÖ±ÏßµÄбÂÊΪk£¬A£¨x1£¬y1£©B£¨x2£¬y2£©£¬G£¨x3£¬y3£©£¬H£¨x4£¬y4£©
¡ßF£¨1£¬0£©£¬¡à$\overrightarrow{AF}=£¨1-{x}_{1}£¬-{y}_{1}£©£¬\overrightarrow{FG}=£¨{x}_{3}-1£¬{y}_{3}£©$
ÓÉ$\overrightarrow{AF}={¦Ë}_{1}\overrightarrow{FG}$£¬µÃ-y1=¦Ë1y3£¬¼´${¦Ë}_{1}=-\frac{{y}_{1}}{{y}_{3}}$
µ±AGÓëxÖá²»´¹Ö±Ê±£¬Ö±ÏßAGµÄ·½³ÌΪ$y=\frac{{y}_{1}}{{x}_{1}-1}£¨x-1£©$
¼´x=$\frac{£¨{x}_{1}-1£©y+{y}_{1}}{{y}_{1}}$£¬´úÈëÍÖÔ²·½³Ì$\frac{{x}^{2}}{2}+{y}^{2}=1$£¬ÕûÀíµÃ£º$£¨3-{2x}_{1}£©{y}^{2}+2{y}_{1}£¨{x}_{1}-1£©y-{y}_{1}^{2}=0$
ÔòÓÐ${y}_{1}{y}_{3}=\frac{-{y}_{1}^{2}}{3-2{x}_{1}}$
¼´$-\frac{{y}_{1}}{{y}_{3}}=3-2{x}_{1}$£¬¡à¦Ë1=3-2x1
µ±AGÓëxÖᴹֱʱ£¬AµãµÄºá×ø±êΪ1£¬¦Ë1=1£¬¦Ë1=3-2x1Ò²³ÉÁ¢
ͬÀí£¬¿ÉµÃ£¬¦Ë2=3-2x2
ÉèÖ±ÏßlµÄ·½³ÌΪy=k£¨x+2£©£¬´úÈë$\frac{{x}^{2}}{2}+{y}^{2}=1$£¬µÃ
£¨2k2+1£©2+8k2x+8k2-2=0
ÒÀÌâÒâµÃ$\left\{\begin{array}{l}{k¡Ù0}\\{¡÷=£¨8{k}^{2}£©^{2}-4£¨2{k}^{2}+1£©£¨8{k}^{2}-2£©£¾0}\end{array}\right.$
½âµÃ$0£¼{k}^{2}£¼\frac{1}{2}$
ÓÖ${x}_{1}+{x}_{2}=-\frac{8{k}^{2}}{2{k}^{2}+1}£¬{x}_{1}{x}_{2}=\frac{8{k}^{2}-2}{2{k}^{2}+1}$
¡à¦Ë1+¦Ë2=3-2x1+3-2x2=6-2£¨x1+x2£©=$6+\frac{16{k}^{2}}{2{k}^{2}+1}$=14-$\frac{8}{2{k}^{2}+1}$
ÓÉ$0£¼{k}^{2}£¼\frac{1}{2}$µÃ£¬6$£¼14-\frac{8}{2{k}^{2}+1}£¼10$£¬¼´6£¼¦Ë1+¦Ë2£¼10
¼´¦Ë1+¦Ë2µÄȡֵ·¶Î§ÊÇ£¨6£¬10£©
£¨ii£©¡ß|AF|=¦Ë1|FG|£¬|BF|=¦Ë2|FH|
¼´|FG|=$\frac{|AF|}{{¦Ë}_{1}}£¬|FH|=\frac{|BF|}{{¦Ë}_{2}}$
´úÈë|AF||GF|=|BF||HF|µÃ
${¦Ë}_{2}|AF{|}^{2}={¦Ë}_{1}|BF{|}^{2}£¨*£©$
ÓÖ|AF|2=£¨1-x1£©2+y12=$£¨1-{x}_{1}£©^{2}+1-\frac{{x}_{1}^{2}}{2}$=2-2${x}_{1}+\frac{1}{2}{x}_{1}^{2}$
ͬÀí|BF|2=2-2x2+$\frac{1}{2}{x}_{2}^{2}$
Ó֡ߦË1=3-2x1£¬¦Ë2=3-2x2£¬´úÈ루*£©µÃ
£¨3-2x2£©£¨2-2x1+$\frac{1}{2}$${x}_{1}^{2}$£©=£¨3-2x1£©£¨2-2x2+$\frac{1}{2}{x}_{2}^{2}$£©
»¯¼òµÃ${x}_{1}-{x}_{2}=\frac{3}{4}£¨{x}_{1}+{x}_{2}£©£¨{x}_{1}-{x}_{2}£©-\frac{1}{2}{x}_{1}{x}_{2}$£¨x1-x2£©
¼´$\frac{3}{4}¡Á£¨-\frac{8{k}^{2}}{2{k}^{2}+1}£©-\frac{1}{2}¡Á\frac{8{k}^{2}-2}{2{k}^{2}+1}=1$
½âµÃk=0£¬ÓëÌâÉèì¶Ü£¬
¹Ê²»´æÔÚÖ±Ïßl£¬Ê¹µÃ|AF|•|GF|=|BF|•|HF|³ÉÁ¢£®

µãÆÀ ±¾ÌâÖ÷Òª¿¼²éÁËÖ±ÏßÓëÔ²×¶ÇúÏßµÄ×ÛºÏÓ¦Óã¬ÄѶȽϴó£¬Ë¼Â·¸´ÔÓ£¬ÐèÒªÓÐÐÛºñµÄ»ù´¡£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

19£®ÒÑÖªº¯Êýy=f£¨x£©ÊÇRÉϵÄżº¯Êý£¬¶ÔÓÚÈÎÒâµÄx¡ÊR£¬¶¼ÓÐf£¨x+4£©=f£¨x£©+f£¨2£©³ÉÁ¢£¬µ±x1£¬x2¡Ê[0£¬2]ÇÒx1¡Ù2ʱ£¬¶¼ÓÐ$\frac{f£¨{x}_{1}£©-f£¨{x}_{2}£©}{{x}_{1}-{x}_{2}}$£¾0£®
ÔòÏÂÁÐÃüÌâÖУ¬ÕýÈ·µÄΪ¢Ù¢Ú¢Ü £¨°ÑÄãÈÏΪÕýÈ·µÄÃüÌâµÄÐòºÅ¶¼ÌîÉÏ£©
¢Ùf£¨2£©=0£»¢ÚÖ±Ïßx=-4ÊǺ¯Êýy=f£¨x£©µÄͼÏóµÄÒ»Ìõ¶Ô³ÆÖ᣻¢Ûº¯Êýy=f£¨x£©ÔÚ[-6£¬-4]ÉÏΪÔöº¯Êý£»¢Üº¯Êýy=f£¨x£©ÔÚ[-6£¬6]ÉÏÓÐËĸöÁãµã£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

20£®Éèx¡¢yÂú×ãÔ¼ÊøÌõ¼þ$\left\{\begin{array}{l}{3x-y-6¡Ü0}\\{x-y+2¡Ý0}\\{x¡Ý0£¬y¡Ý0}\end{array}\right.$Ä¿±êº¯Êýz=2x+yµÄ×î´óÖµÊÇ14£¬ÈôÄ¿±êº¯Êýz=ax+by£¨a£¾0£¬b£¾0£©µÄ×î´óֵΪ10£¬Ôò$\frac{2}{a}$+$\frac{3}{b}$µÄ×îСֵΪ5£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

17£®ÒÑÖªÃݺ¯Êýy=f£¨x£©Í¼Ïó¹ýµã£¨2£¬$\sqrt{2}$£©£¬Ôò¸ÃÃݺ¯ÊýµÄÖµÓòÊÇ[0£¬+¡Þ£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

1£®ÒÑÖªÍÖÔ²M£º$\frac{x^2}{4}+\frac{y^2}{3}$=1£¬µãF1£¬C·Ö±ðÊÇÍÖÔ²MµÄ×󽹵㡢×󶥵㣬¹ýµãF1µÄÖ±Ïßl£¨²»ÓëxÖáÖØºÏ£©½»MÓÚA£¬BÁ½µã£®
£¨¢ñ£©ÇóMµÄÀëÐÄÂʼ°¶ÌÖ᳤£»
£¨¢ò£©ÊÇ·ñ´æÔÚÖ±Ïßl£¬Ê¹µÃµãBÔÚÒÔÏß¶ÎACΪֱ¾¶µÄÔ²ÉÏ£¬Èô´æÔÚ£¬Çó³öÖ±ÏßlµÄ·½³Ì£»Èô²»´æÔÚ£¬ËµÃ÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

11£®ÒÑÖªº¯Êýf£¨x£©=£¨x2+ax+a£©ex£¨a¡Ü2£¬x¡ÊR£©
£¨1£©Èôa=1£¬Çóy=f£¨x£©Ôڵ㣨0£¬f£¨0£©£©´¦µÄÇÐÏß·½³Ì£»
£¨2£©ÊÇ·ñ´æÔÚʵÊýa£¬Ê¹µÃf£¨x£©µÄ¼«´óֵΪ3£¬Èô´æÔÚ£¬Çó³öaµÄÖµ£»Èô²»´æÔÚ£¬ËµÃ÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

18£®Ô²x2+£¨y+1£©2=5Éϵĵ㵽ֱÏß2x-y+9=0µÄ×î´ó¾àÀëΪ3$\sqrt{5}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

15£®¸´Êý$z=\frac{i}{1-i}$ÔÚ¸´Æ½ÃæÉϱíʾµÄµãÔÚµÚ£¨¡¡¡¡£©ÏóÏÞ£®
A£®Ò»B£®¶þC£®ÈýD£®ËÄ

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

16£®Èçͼ£¬CEΪԲOµÄÖ±¾¶£¬PEΪԲOµÄÇÐÏߣ¬EΪÇе㣬PBAΪԲOµÄ¸îÏߣ¬½»CEÓÚDµã£¬CD=2£¬AD=3£¬BD=4£¬ÔòÔ²OµÄ°ë¾¶Îªr=4£»PB=20£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸