7£®ÒÑÖªÍÖÔ²$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄ×ó¡¢ÓÒÁ½¸ö½¹µã·Ö±ðΪF1£¬F2£¬ÀëÐÄÂÊe=$\frac{\sqrt{2}}{2}$£¬¶ÌÖ᳤Ϊ2£®
£¨¢ñ£©ÇóÍÖÔ²µÄ·½³Ì£»
£¨¢ò£©ÉèµãAΪÍÖÔ²ÉϵÄÒ»¶¯µã£¨·Ç³¤Öá¶Ëµã£©£¬AF1µÄÑÓ³¤ÏßÓëÍÖÔ²½»ÓÚBµã£¬AOµÄÑÓ³¤ÏßÓëÍÖÔ²½»ÓÚCµã£¬Èô¡÷ABCÃæ»ýΪ$\frac{\sqrt{6}}{2}$£¬ÇóÖ±ÏßABµÄ·½³Ì£®

·ÖÎö £¨¢ñ£©ÓÉÀëÐÄÂÊe=$\frac{\sqrt{2}}{2}$£¬¶ÌÖ᳤Ϊ2£®¿ÉµÃa£¬b£¬¼´¿Éд³ö·½³Ì£»
£¨¢ò£©¢Ùµ±Ö±ÏßlбÂʲ»´æÔÚʱ£¬²»·ÁÈ¡A£¨1£¬$\frac{\sqrt{2}}{2}$£©£¬B£¨1£¬-$\frac{\sqrt{2}}{2}$£©£¬C£¨-1£¬-$\frac{\sqrt{2}}{2}$£©£¬²»·ûºÏÌâÒ⣮
¢Úµ±Ö±Ïß lбÂÊ´æÔÚʱ£¬ÉèÖ±ÏßAB£ºy=k£¨x-1£©£¬ÓÉ$\left\{\begin{array}{l}{y=k£¨x-1£©}\\{\frac{{x}^{2}}{2}+{y}^{2}=1}\end{array}\right.$»¯¼òµÃ £¨2k2+1£©x2-4k2x+2k2-2=0£¬ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬¿ÉµÃ|AB|=$\sqrt{£¨1{+k}^{2}£©[£¨{x}_{1}+{x}_{2}£©^{2}-4{x}_{1}{x}_{2}}$=$2\sqrt{2}\frac{{k}^{2}+1}{2{k}^{2}+1}$
 µãOµ½Ö±Ïßkx-y-k=0µÄ¾àÀëd=$\frac{|k|}{\sqrt{{k}^{2}+1}}$£¬¡÷ABCÃæ»ýΪs=$\frac{1}{2}$|AB|¡Á2d=2$\sqrt{2}$¡Á$\frac{\sqrt{{k}^{4}+{k}^{2}}}{2{k}^{2}+1}$=$\frac{\sqrt{6}}{2}$£®k=¡À$\frac{\sqrt{2}}{2}$£¬¼´¿ÉµÃÖ±ÏßABµÄ·½³Ì

½â´ð ½â£º£¨¢ñ£©ÓÉÌâÒâµÃ2b=2£¬¡àb=1£¬

¡ß$\frac{c}{a}=\frac{\sqrt{2}}{1}$£¬a2=b2+c2£¬¡àa=$\sqrt{2}$£¬c=1£¬
¡àÍÖÔ²µÄ·½³ÌΪ$\frac{{x}^{2}}{2}+{y}^{2}=1$£®
£¨¢ò£©¢Ùµ±Ö±ÏßlбÂʲ»´æÔÚʱ£¬²»·ÁÈ¡A£¨1£¬$\frac{\sqrt{2}}{2}$£©£¬B£¨1£¬-$\frac{\sqrt{2}}{2}$£©£¬C£¨-1£¬-$\frac{\sqrt{2}}{2}$£©
¡à¡÷ABCÃæ»ýΪS=$\frac{1}{2}¡Á2¡Á\sqrt{2}$=$\sqrt{2}$£¬²»·ûºÏÌâÒ⣮
¢Úµ±Ö±Ïß lбÂÊ´æÔÚʱ£¬ÉèÖ±ÏßAB£ºy=k£¨x-1£©£¬
ÓÉ$\left\{\begin{array}{l}{y=k£¨x-1£©}\\{\frac{{x}^{2}}{2}+{y}^{2}=1}\end{array}\right.$»¯¼òµÃ £¨2k2+1£©x2-4k2x+2k2-2=0
ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬Ôò${x}_{1}+{x}_{2}=\frac{4{k}^{2}}{2{k}^{2}+1}$£¬${x}_{1}{x}_{2}=\frac{2{k}^{2}-2}{2{k}^{2}+1}$£®
¡à|AB|=$\sqrt{£¨1{+k}^{2}£©[£¨{x}_{1}+{x}_{2}£©^{2}-4{x}_{1}{x}_{2}}$=$2\sqrt{2}\frac{{k}^{2}+1}{2{k}^{2}+1}$
¡ßµãOµ½Ö±Ïßkx-y-k=0µÄ¾àÀëd=$\frac{|k|}{\sqrt{{k}^{2}+1}}$£¬
ÓÖOÊÇÏß¶ÎACµÄÖе㣬¡àµãCµ½Ö±ÏßABµÄ¾àÀë2d=2¡Á$\frac{|k|}{\sqrt{{k}^{2}+1}}$
¡à¡÷ABCÃæ»ýΪs=$\frac{1}{2}$|AB|¡Á2d=2$\sqrt{2}$¡Á$\frac{\sqrt{{k}^{4}+{k}^{2}}}{2{k}^{2}+1}$=$\frac{\sqrt{6}}{2}$£®
¡à4k4+4k2-3=0£¬½âµÃ${k}^{2}=\frac{1}{2}$£¬k=¡À$\frac{\sqrt{2}}{2}$
¡àÖ±ÏßABµÄ·½³ÌΪy=$\frac{\sqrt{2}}{2}$£¨x-1£©»òy=-$\frac{\sqrt{2}}{2}£¨x-1£©$£®

µãÆÀ ±¾Ì⿼²éÁËÍÖÔ²µÄ·½³Ì£¬Ö±ÏßÓëÍÖÔ²µÄλÖùØÏµ£¬¿¼²éÁ˵㵽ֱÏߵľàÀ빫ʽ¡¢Ãæ»ý¼ÆË㣬ÔËËãÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

17£®Æ½ÃæÉÏ£¬µãA¡¢CΪÉäÏßPMÉϵÄÁ½µã£¬µãB¡¢DΪÉäÏßPNÉϵÄÁ½µã£¬ÔòÓÐ$\frac{{{S_{¡÷PAB}}}}{{{S_{¡÷PCD}}}}=\frac{PA•PB}{PC•PD}$£¨ÆäÖÐS¡÷PAB¡¢S¡÷PCD·Ö±ðΪ¡÷PAB¡¢¡÷PCDµÄÃæ»ý£©£»¿Õ¼äÖУ¬µãA¡¢CΪÉäÏßPMÉϵÄÁ½µã£¬µãB¡¢DΪÉäÏßPNÉϵÄÁ½µã£¬µãE¡¢FΪÉäÏßPLÉϵÄÁ½µã£¬ÔòÓÐ$\frac{{{V_{P-ABE}}}}{{{V_{P-CDF}}}}$=$\frac{PA•PB•PE}{PC•PD•PF}$£¨ÆäÖÐVP-ABE¡¢VP-CDF·Ö±ðΪËÄÃæÌåP-ABE¡¢P-CDFµÄÌå»ý£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

18£®ÒÑÖªµãP£¨x£¬y£©Âú×ãÌõ¼þ$\sqrt{{{£¨x+1£©}^2}+{y^2}}+\sqrt{{{£¨x-1£©}^2}+{y^2}}=4$£®
£¨¢ñ£©ÇóµãPµÄ¹ì¼£CµÄ·½³Ì£»
£¨¢ò£©Ö±ÏßlÓëÔ²O£ºx2+y2=1ÏàÇУ¬ÓëÇúÏßCÏà½ÏÓÚA£¬BÁ½µã£¬Èô$\overrightarrow{OA}•\overrightarrow{OB}=-\frac{4}{3}$£¬ÇóÖ±ÏßlµÄбÂÊ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

15£®ÔÚËÄÀâÖùABCD-A1B1C1D1ÖУ¬ËıßÐÎABCDΪƽÐÐËıßÐΣ¬AA1¡ÍÆ½ÃæABCD£¬¡ÏBAD=60¡ã£¬AB=2£¬BC=1£®AA1=$\sqrt{6}$£¬EΪA1B1µÄÖе㣮
£¨1£©ÇóÖ¤£ºÆ½ÃæA1BD¡ÍÆ½ÃæA1AD£»
£¨2£©Çó¶àÃæÌåA1E-ABCDµÄÌå»ý£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

2£®ÒÑÖª¼¯ºÏA={x|3¡Üx£¼7}£¬B={x|2£¼x£¼10}£¬Ôò∁R£¨A¡ÈB£©=£¨¡¡¡¡£©
A£®{x|3¡Üx£¼7}£¬B£®{x|2£¼x£¼10}C£®{x|x¡Ü2»òx¡Ý10}D£®{x|x£¼3»òx¡Ý7}

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

12£®ÒÑÖªÊýÁÐ{an}µÄǰnÏîºÍΪSn£¬Sn=2an-3£®
£¨¢ñ£©ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨¢ò£©ÇóÊýÁÐ{nan}µÄǰnÏîºÍTn£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®ÒÑÖªº¯Êý$f£¨x£©=1-\frac{1}{2}|x-2|$£¬Ôòº¯Êý$g£¨x£©=f£¨x£©-cos\frac{¦Ð}{2}x$ÔÚÇø¼ä[-6£¬6]ËùÓÐÁãµãµÄºÍΪ£¨¡¡¡¡£©
A£®6B£®8C£®12D£®16

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

16£®ÒÑÖª¼¯ºÏA={x|x2-3x-4£¾0}£¬B={x||x|¡Ü3}£¬ÔòA¡ÉB=£¨¡¡¡¡£©
A£®[3£¬4£©B£®£¨-4£¬-3]C£®£¨1£¬3]D£®[-3£¬-1£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

17£®ÒÑÖªº¯Êý$f£¨x£©=Asin£¨{¦Øx+¦Õ}£©£¨{A£¾0£¬¦Ø£¾0£¬0£¼¦Õ£¼\frac{¦Ð}{2}}£©$µÄ²¿·ÖͼÏóÈçͼËùʾ£¬½«f£¨x£©µÄͼÏóÏòÓÒÆ½ÒÆ$\frac{¦Ð}{6}$¸öµ¥Î»µÃµ½º¯Êýg£¨x£©µÄͼÏó£®
£¨I£©Çóº¯Êýg£¨x£©µÄ½âÎöʽ¼°µ¥µ÷µÝÔöÇø¼ä£»
£¨II£©ÔÚ¡÷x ABCÖУ¬½ÇA£¬B£¬CµÄ¶Ô±ß·Ö±ðΪa£¬b£¬c£¬Èô£¨2a-c£©cosB-bcosC=0ÇÒ$f£¨{\frac{A}{2}}£©=\frac{2}{3}$£¬Çócos£¨A-B£©µÄÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸