15£®ÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÉ϶¥µãΪA£¬P£¨$\frac{4\sqrt{2}}{3}$£¬$\frac{b}{3}$£©ÊÇÍÖÔ²CÉϵÄÒ»µã£¬ÒÔAPΪֱ¾¶µÄÔ²¾­¹ýÍÖÔ²CµÄÓÒ½¹µãF2£®
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨2£©ÉèF1ΪÍÖÔ²CµÄ×󽹵㣬¹ýÓÒ½¹µãF2µÄÖ±ÏßlÓëÍÖÔ²C½»ÓÚ²»Í¬Á½µãM¡¢N£¬¼Ç¡÷F1MNµÄÄÚÇÐÔ²µÄÃæ»ýΪS£¬Çóµ±SÈ¡×î´óֵʱֱÏßlµÄ·½³Ì£¬²¢Çó³ö×î´óÖµ£®

·ÖÎö £¨1£©ÓÉÍÖÔ²µÄÉ϶¥µãΪA£¬ÒÔAPΪֱ¾¶µÄÔ²¾­¹ýÍÖÔ²CµÄÓÒ½¹µãF2£®P£¨$\frac{4\sqrt{2}}{3}$£¬$\frac{b}{3}$£©ÊÇÍÖÔ²CÉϵÄÒ»µã£¬Áгö·½³Ì×飬Çó³öa£¬b£¬ÓÉ´ËÄÜÇó³öÍÖÔ²CµÄ·½³Ì£®
£¨2£©ÉèÖ±ÏßlµÄ·½³ÌΪx=my+$\sqrt{2}$£¬ÓÉ$\left\{\begin{array}{l}{x=my+\sqrt{2}}\\{{x}^{2}+2{y}^{2}=4}\end{array}\right.$£¬µÃ$£¨{m}^{2}+2£©{y}^{2}+2\sqrt{2}my-2=0$£¬ÓÉ´ËÀûÓÃΤ´ï¶¨Àí¡¢ÍÖÔ²¶¨Ò塢ҪʹÄÚÇÐÔ²Ãæ»ýS×î´ó£¬Ö»ÐèÒªÇó¡÷F1MNµÄÃæ»ýS¡ä×î´ó£¬½áºÏÒÑÖªÌõ¼þÄÜÇó³öµ±SÈ¡×î´óֵʱֱÏßlµÄ·½³Ì£¬²¢ÄÜÇó³ö×î´óÖµ£®

½â´ð ½â£º£¨1£©¡ßÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÉ϶¥µãΪA£¬ÒÔAPΪֱ¾¶µÄÔ²¾­¹ýÍÖÔ²CµÄÓÒ½¹µãF2£®
¡àF2£¨c£¬0£©£¬A£¨0£¬b£©£¬P£¨$\frac{4\sqrt{2}}{3}£¬\frac{b}{3}$£©£¬
¡à$\overrightarrow{{F}_{2}A}•\overrightarrow{{F}_{2}P}$=£¨-c£¬b£©•£¨$\frac{4\sqrt{2}}{3}$-c£¬$\frac{b}{3}$£©=c2-$\frac{4\sqrt{2}}{3}c$+$\frac{{b}^{2}}{3}$=0£¬
¡ßP£¨$\frac{4\sqrt{2}}{3}$£¬$\frac{b}{3}$£©ÊÇÍÖÔ²CÉϵÄÒ»µã£¬
¡à$\frac{32}{9{a}^{2}}+\frac{{b}^{2}}{9{b}^{2}}=1$£¬½âµÃa=2£¬
¡ßa2=b2+c2£¬½âµÃc=$\sqrt{2}$£¬b=$\sqrt{2}$£¬
¡àÍÖÔ²CµÄ·½³ÌΪ$\frac{{x}^{2}}{4}+\frac{{y}^{2}}{2}$=1£®
£¨2£©ÓÉÌâÒâÖ±ÏßlµÄбÂʲ»Îª0£¬ÉèÖ±ÏßlµÄ·½³ÌΪx=my+$\sqrt{2}$£¬A£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬
ÓÉ$\left\{\begin{array}{l}{x=my+\sqrt{2}}\\{{x}^{2}+2{y}^{2}=4}\end{array}\right.$£¬µÃ$£¨{m}^{2}+2£©{y}^{2}+2\sqrt{2}my-2=0$£¬
y1+y2=$\frac{-2\sqrt{2}m}{{m}^{2}+2}$£¬y1y2=$\frac{-2}{{m}^{2}+2}$£¬
ÉèÄÚÇÐÔ²µÄ°ë¾¶Îªr£¬¡÷F1MNµÄÖܳ¤ÎªC£¬Ãæ»ýΪS¡ä£¬
¡ßS¡ä=$\frac{1}{2}Cr$£¬
ÓÉÍÖÔ²¶¨ÒåµÃC=4a=8£¬¡àS¡ä=4r£¬
ҪʹÄÚÇÐÔ²Ãæ»ýS×î´ó£¬Ö»ÐèÒªÇó¡÷F1MNµÄÃæ»ýS¡ä×î´ó£¬
¡÷F1MNµÄÃæ»ýΪ£º
S¡ä=$\frac{1}{2}¡Á2c¡Á|{y}_{1}-{y}_{2}|$=$\sqrt{2}\sqrt{£¨{y}_{1}+{y}_{2}£©^{2}-4{y}_{1}{y}_{2}}$
=$\sqrt{2[£¨\frac{-2\sqrt{2}m}{{m}^{2}+2}£©^{2}-4•\frac{-2}{{m}^{2}+2}]}$=$\frac{4\sqrt{2}•\sqrt{{m}^{2}+1}}{{m}^{2}+2}$£¬
Áît=$\sqrt{{m}^{2}+1}$£¬t¡Ý1£®
S¡ä=$\frac{4\sqrt{2}t}{{t}^{2}+1}$=$\frac{4\sqrt{2}}{t+\frac{1}{t}}$$¡Ü2\sqrt{2}$£¬
µ±ÇÒ½öµ±t=1£¬¼´m=0ʱȡµÈºÅ£¬
´Ëʱr=$\frac{\sqrt{2}}{2}$£¬S=¦Ðr2=$\frac{¦Ð}{2}$£¬
Ö±ÏßlµÄ·½³ÌΪx=$\sqrt{2}$£®

µãÆÀ ±¾Ì⿼²éÍÖÔ²·½³ÌµÄÇ󷨣¬¿¼²éµ±Èý½ÇÐεÄÄÚÇÐÔ²µÄÃæ»ýÈ¡×î´óֵʱֱÏßlµÄ·½³Ì¼°Õâ¸ö×î´óÖµµÄÇ󷨣¬ÊÇÖеµÌ⣬½âÌâʱҪÈÏÕæÉóÌ⣬עÒâ¸ùµÄÅбðʽ¡¢Î¤´ï¶¨Àí¡¢ÏÒ³¤¹«Ê½¡¢µãµ½Ö±Ïß¾àÀ빫ʽ¡¢ÍÖÔ²ÐÔÖʵĺÏÀíÔËÓã®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

5£®Èçͼ£¬ÈýÀâÖùABC-A1B1C1ÖУ¬¡ÏB1A1A=¡ÏC1A1A=60¡ã£¬AA1=AC=4£¬AB=2£¬P£¬Q·Ö±ðΪÀâAA1£¬ACµÄÖе㣮
£¨1£©ÔÚƽÃæABCÄÚ¹ýµãA×÷AM¡ÎƽÃæPQB1½»BCÓÚµãM£¬²¢Ð´³ö×÷ͼ²½Ö裬µ«²»ÒªÇóÖ¤Ã÷£»
£¨2£©Èô²àÃæACC1A1¡Í²àÃæABB1A1£¬ÇóÖ±ÏßA1C1ÓëƽÃæPQB1Ëù³É½ÇµÄÕýÏÒÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

6£®ÒÑÖªº¯Êýf£¨x£©=ax-1£¨a£¾0£¬ÇÒa¡Ù1£©Âú×ãf£¨1£©£¾1£¬Èôº¯Êýg£¨x£©=f£¨x+1£©-4µÄͼÏó²»¹ýµÚ¶þÏóÏÞ£¬ÔòaµÄÈ¡Öµ·¶Î§ÊÇ£¨¡¡¡¡£©
A£®£¨2£¬+¡Þ£©B£®£¨2£¬5]C£®£¨1£¬2£©D£®£¨1£¬5]

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

3£®Èôº¯Êýf£¨2x+1£©µÄ¶¨ÒåÓòΪ£¨-1£¬0£©£¬Ôòº¯Êýf£¨x£©µÄ¶¨ÒåÓòΪ£¨¡¡¡¡£©
A£®£¨-2£¬0£©B£®£¨-1£¬0£©C£®£¨-1£¬1£©D£®£¨0£¬1£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

10£®ÒÑÖªº¯Êýy=f£¨x£©ÎªRÉϵÄÆ溯Êý£¬ÆäÁãµãΪx1£¬x2£¬¡­£¬x2017£¬Ôòx1+x2+¡­+x2017=0£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

20£®¸ø¶¨ËÄ×éÊý¾Ý£º¼×£º1£¬2£¬3£¬4£¬5£»ÒÒ£º1£¬3£¬5£¬7£¬9£»±û£º1£¬2£¬3£»¶¡£º1£¬3£¬5£®ÆäÖз½²î×îСµÄÒ»×éÊÇ£¨¡¡¡¡£©
A£®¼×B£®ÒÒC£®±ûD£®¶¡

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

7£®Ä³ÈË´òËãÖƶ¨Ò»¸ö³¤ÆÚ´¢Ðî¼Æ»®£¬Ã¿ÄêÄê³õ´æ¿î2ÍòÔª£¬Á¬Ðø´¢Ðî12Ä꣮ÓÉÓÚ×ʽðÔ­Òò£¬´ÓµÚ7ÄêÄê³õ¿ªÊ¼£¬±ä¸üΪÿÄêÄê³õ´æ¿î1ÍòÔª£®Èô´æ¿îÀûÂÊΪÿÄê2%£¬ÇÒÉÏÒ»ÄêÄêÄ©µÄ±¾Ï¢ºÍ¹²Í¬×÷ΪÏÂÒ»ÄêÄê³õµÄ±¾½ð£¬ÔòµÚ13ÄêÄê³õµÄ±¾Ï¢ºÍԼΪ20.9ÍòÔª£¨½á¹û¾«È·µ½0.1£©£®£¨²Î¿¼Êý¾Ý£º1.026¡Ö1.13£¬1.0212¡Ö1.27£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

4£®Ä³¼¸ºÎÌåÉϵÄÈýÊÓͼÈçͼËùʾ£¬Ôò¸Ã¼¸ºÎÌåµÄÌå»ýÊÇ$\frac{4+¦Ð}{3}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

5£®ÔÚƽÃæÖ±½Ç×ø±êϵÖУ¬ÒÑÖªµãM£¨1£¬0£©£¬P£¨x£¬y£©ÎªÆ½ÃæÉÏÒ»¶¯µã£¬Pµ½Ö±Ïßx=2µÄ¾àÀëΪd£¬$\frac{|PM|}{d}$=$\frac{\sqrt{2}}{2}$£®
£¨¢ñ£©ÇóµãPµÄ¹ì¼£CµÄ·½³Ì£»
£¨¢ò£©²»¹ýÔ­µãOµÄÖ±ÏßlÓëCÏཻÓÚA£¬BÁ½µã£¬Ï߶ÎABµÄÖеãΪD£¬Ö±ÏßODÓëÖ±Ïßx=2½»µãµÄ×Ý×ø±êΪ1£¬Çó¡÷OABÃæ»ýµÄ×î´óÖµ¼°´ËʱֱÏßlµÄ·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸