2£®ÒÑÖªÍÖÔ²$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©¾­¹ýµãM£¨1£¬$\frac{\sqrt{6}}{2}$£©£¬ÇÒÀëÐÄÂÊΪ$\frac{\sqrt{2}}{2}$£®
£¨1£©ÇóÍÖÔ²µÄ±ê×¼·½³Ì£»
£¨2£©ÈôP£¨-1£¬$\frac{1}{2}$£©ÊÇÍÖÔ²ÄÚÒ»µã£¬ÍÖÔ²µÄÄÚ½ÓÌÝÐÎABCD£¬£¨AB¡ÎCD£©µÄ¶Ô½ÇÏßACÓëBD½»ÓÚµãP£¬ÉèÖ±ÏßABÔÚyÖáÉϵĽؾàΪm£¬¼Çf£¨m£©=S¡÷PAB£¬Çóf£¨m£©µÄ±í´ïʽ
£¨3£©Çóg£¨m£©=[f£¨m£©]2-$\frac{2}{3}$m3+4m-3µÄ×î´óÖµ£®

·ÖÎö £¨1£©Í¨¹ý½«µãM£¨1£¬$\frac{\sqrt{6}}{2}$£©´úÈëÍÖÔ²·½³Ì£¬ÀûÓÃÀëÐÄÂÊΪ$\frac{\sqrt{2}}{2}$£¬¼ÆËã¼´µÃ½áÂÛ£»
£¨2£©Í¨¹ýÉèÖ±ÏßAB¡¢CDµÄ·½³Ì£¬²¢·Ö±ðÓëÍÖÔ²·½³ÌÁªÁ¢£¬ÀûÓÃΤ´ï¶¨Àí¡¢A¡¢C¡¢PÈýµã¹²Ïß¡¢B¡¢D¡¢PÈýµã¹²Ïß¡¢Á½µã¼ä¾àÀ빫ʽ¡¢Èý½ÇÐÎÃæ»ý¹«Ê½¼ÆËã¼´µÃ½áÂÛ£»
£¨3£©ÀûÓûù±¾²»µÈʽ¼ÆËã¼´µÃ½áÂÛ£®

½â´ð ½â£º£¨1£©¡ßÍÖÔ²$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©¾­¹ýµãM£¨1£¬$\frac{\sqrt{6}}{2}$£©£¬
¡à$\frac{1}{{a}^{2}}+\frac{6}{4{b}^{2}}=1$£¬
ÓÖ¡ßÀëÐÄÂÊΪ$\frac{\sqrt{2}}{2}$£¬
¡àe=$\frac{c}{a}$=$\frac{\sqrt{{a}^{2}-{b}^{2}}}{a}$=$\frac{\sqrt{2}}{2}$£¬¼´£ºa2=2b2£¬
¡àa2=4£¬b2=2£¬
¡àÍÖÔ²µÄ±ê×¼·½³ÌΪ£º$\frac{{x}^{2}}{4}+\frac{{y}^{2}}{2}=1$£»
£¨2£©ÓÉÒÑÖªµÃAB¡¢CD²»´¹Ö±ÓÚxÖᣨ·ñÔòÓɶԳÆÐÔ£¬µãPÔÚxÖáÉÏ£©£¬
ÉèÖ±ÏßABµÄ·½³ÌΪy=kx+m£¬Ö±ÏßCDµÄ·½³ÌΪy=kx+n£¨m¡Ùn£©£¬
½«y=kx+m´úÈë$\frac{{x}^{2}}{4}+\frac{{y}^{2}}{2}=1$µÃ£º£¨1+2k2£©x2+4kmx+2£¨m2-2£©=0£¬
¡÷=4£¨8k2-2m2+4£©£¾0£¬
ÉèµãA£¨xA£¬yA£©£¬B£¨xB£¬yB£©£¬ÓÉΤ´ï¶¨ÀíµÃ$\left\{\begin{array}{l}{{x}_{A}+{x}_{B}=-\frac{4km}{1+2{k}^{2}}}\\{{x}_{A}{•x}_{B}=\frac{2£¨{m}^{2}-2£©}{1+2{k}^{2}}}\end{array}\right.$£¬

ͬÀíÉèµãC£¨xC£¬yC£©£¬D£¨xD£¬yD£©£¬ÓÉΤ´ï¶¨ÀíµÃ$\left\{\begin{array}{l}{{x}_{C}+{x}_{D}=-\frac{4kn}{1+2{k}^{2}}}\\{{x}_{C}•{x}_{D}=\frac{2£¨{n}^{2}-2£©}{1+2{k}^{2}}}\end{array}\right.$£¬
ÓÉA¡¢C¡¢PÈýµã¹²Ïß¿ÉÖª£º£¨-1-xA£©•£¨$\frac{1}{2}$-yC£©=£¨-1-xC£©•£¨$\frac{1}{2}$-yA£©£¬
»¯¼òµÃ£º-xA+2yC+2xAyC=-xC+2yA+2xCyA£¬
ͬÀíB¡¢D¡¢PÈýµã¹²Ïß¿ÉÖª£º-xB+2yD+2xByD=-xD+2yB+2xDyB£¬
Á½Ê½Ïà¼Ó½áºÏAB¡¢CDµÄ·½³Ìy=kx+m£¬y=kx+n£¨m¡Ùn£©µÃ£º
-£¨xA+xB£©+2k£¨xC+xD£©+2xByD+4n+2xA£¨kxC+n£©+2xB£¨kxD+n£©
=-£¨xC+xD£©+2k£¨xA+xB£©+2xByD+4m+2xC£¨kxA+m£©+2xD£¨kxB+m£©-£¨xA+xB£©+2k£¨xC+xD£©+4n+2n£¨xA+xB£©
=-£¨xC+xD£©+2k£¨xA+xB£©+4m+2m£¨xC+xD£©£¬
ÀûÓÃn£¨xA+xB£©=m£¨xC+xD£©µÃ£º£¨1+2k£©£¨xC+xD£©-£¨xA+xB£©+4£¨n-m£©=0£¬
$\frac{4k£¨1+2k£©£¨m-n£©}{1+2{k}^{2}}$+4£¨n-m£©=0£¬
ÓÉm¡Ùn¿ÉÖªk=1£¬
ÓÉ¡÷¼°Ö±Ïß²»¹ýµãP£¨-1£¬$\frac{1}{2}$£©µÃ£º-$\sqrt{6}$£¼m£¼$\sqrt{6}$ÇÒm¡Ù$\frac{3}{2}$£¬
ÓÖµãP£¨-1£¬$\frac{1}{2}$£©µ½Ö±Ïßx-y+m=0µÄ¾àÀëÊÇd=$\frac{|2m-3|}{2\sqrt{2}}$£¬
¹Êf£¨m£©=S¡÷PAB=$\frac{1}{2}¡Á\sqrt{2}¡Á$$\frac{\sqrt{48-8{m}^{2}}}{3}$¡Á$\frac{|2m-3|}{2\sqrt{2}}$=$\frac{\sqrt{12-2{m}^{2}}}{6}$|2m-3|£¨-$\sqrt{6}$£¼m£¼$\sqrt{6}$ÇÒm¡Ù$\frac{3}{2}$£©£»
£¨3£©g£¨m£©=[f£¨m£©]2-$\frac{2}{3}$m3+4m-3
=-$\frac{2}{9}$m4+$\frac{5}{6}$m2=$\frac{1}{72}$•4m2£¨15-4m2£©
¡Ü$\frac{1}{72}$[$\frac{4{m}^{2}+£¨15-4{m}^{2}£©}{2}$]2=$\frac{25}{32}$£¬
µ±ÇÒ½öµ±4m2=15-4m2¼´m=¡À$\frac{\sqrt{15}}{4}$¡Ê£¨-$\sqrt{6}$£¬$\frac{3}{2}$£©¡È£¨$\frac{3}{2}$£¬$\sqrt{6}$£©Ê±£¬ÉÏʽµÈºÅ³ÉÁ¢£¬
¹Êg£¨m£©µÄ×î´óֵΪ$\frac{25}{32}$£®

µãÆÀ ±¾ÌâÊÇÒ»µÀÖ±ÏßÓëÔ²×¶ÇúÏßµÄ×ÛºÏÌ⣬¿¼²éÔËËãÇó½âÄÜÁ¦£¬Éæ¼°»ù±¾²»µÈʽ¡¢Î¤´ï¶¨Àí¡¢Á½µã¼ä¾àÀ빫ʽµÈ»ù´¡ÖªÊ¶£¬×¢Òâ½âÌâ·½·¨µÄ»ýÀÛ£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

12£®ÒÑÖª¡ÏACB=90¡ã£¬¡ÏACBËùÔÚÆ½ÃæÍâÓÐÒ»µãP£¬PC=24cm£¬µãPµ½¡ÏACBÁ½±ßµÄ¾àÀë¾ùΪ6$\sqrt{10}$cm£¬ÇóPCÓëÆ½ÃæABCËù³ÉµÄ½Ç£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

13£®ÒÑÖª£º¹ýÅ×ÎïÏßx2=4yµÄ½¹µãFµÄÖ±Ïß½»Å×ÎïÏßÓÚA£¬BÁ½¸ö²»Í¬µÄµã£¬¹ýA£¬B·Ö±ð×÷Å×ÎïÏßµÄÇÐÏߣ¬ÇÒ¶þÕßÏཻÓÚµãC£®
£¨1£©ÇóÖ¤£º$\overrightarrow{AB}$•$\overrightarrow{CF}$=0£»
£¨2£©Çó¡÷ABCµÄÃæ»ýµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

10£®¹ý¶¨µãP£¨0£¬2£©×÷Ö±Ïßl£¬Ê¹lÓëÇúÏßy2=4xÓÐÇÒ½öÓÐ1¸ö¹«¹²µã£¬ÕâÑùµÄÖ±Ïßl¹²ÓУ¨¡¡¡¡£©
A£®1ÌõB£®2ÌõC£®3ÌõD£®4Ìõ

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

17£®ÉèÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$ £¨a£¾b£¾0£©µÄÀëÐÄÂÊΪ$\frac{\sqrt{2}}{2}$£¬ÈôÖÐ×ó½¹µãΪF£¨-2£¬0£©
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì
£¨2£©ÈôбÂÊΪ1µÄÖ±Ïß¹ýÍÖÔ²CµÄÓÒ½¹µãÇÒÓëÍÖÔ²½»ÓÚA£¬BÁ½µã£¬Çó|AB|µÄ³¤£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

7£®ÒÑÖªÍÖÔ²µÄ³¤Ö᳤Êǽ¹¾àµÄ2±¶£¬ÔòÍÖÔ²µÄÀëÐÄÂÊΪ$\frac{1}{2}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

14£®¹ýÍÖÔ²$\frac{{x}^{2}}{16}$+$\frac{{y}^{2}}{9}$=1µÄ×ó½¹µãF1µÄÖ±Ïß½»ÍÖÔ²ÓÚA£¬BÁ½µã£¬F2ÊÇÓÒ½¹µã£¬Ôò¡÷ABF2µÄÖܳ¤ÊÇ£¨¡¡¡¡£©
A£®6B£®8C£®12D£®16

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

11£®Èçͼ£¬ÔÚÆÂ¶ÈÒ»¶¨µÄɽÆÂÉϵÄÒ»µãA´¦£¬²âµÃɽ¶¥ÉÏÒ»½¨ÖþÎïCDµÄ¶¥¶ËC¶ÔÓÚɽÆÂµÄб¶ÈΪ15¡ã£¬Ïòɽ¶¥Ç°½ø75Ã×µ½´ïBµã£¬ÔٴβâÁ¿µÃÆäб¶ÈΪ30¡ã£¬¼ÙÉ轨ÖþÎï¸ß50Ã×£¬ÉèɽÆÂ¶ÔÓÚË®Æ½ÃæµÄб¶ÈΪ¦È£¬Ôòcos¦È=$\frac{3}{4}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

12£®Èç¹ûÖ´ÐÐÓұߵijÌÐò¿òͼ£¬ÈôÊäÈëx=-11£¬ÄÇôÆäÊä³öµÄ½á¹ûÊÇ£¨¡¡¡¡£©
A£®0B£®1C£®2D£®3

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸