1£®ÒÑÖªÍÖÔ²Cn£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=n£¨a£¾b£¾1£¬n¡ÊN*£©£¬F1£¬F2ÊÇÍÖÔ²C4µÄ½¹µã£¬A£¨2£¬$\sqrt{2}$£©ÊÇÍÖÔ²C4ÉÏÒ»µã£¬ÇÒ$\overrightarrow{A{F}_{2}}$?$\overrightarrow{{F}_{1}{F}_{2}}$=0£»
£¨1£©ÇóCnµÄÀëÐÄÂʲ¢Çó³öC1µÄ·½³Ì£»
£¨2£©PΪÍÖÔ²C2ÉÏÈÎÒâÒ»µã£¬Ö±ÏßPF1½»ÍÖÔ²C4ÓÚµãE£¬F£¬Ö±ÏßPF2½»ÍÖÔ²C4ÓÚµãM£¬N£¬ÉèÖ±ÏßPF1µÄбÂÊΪk1£¬Ö±ÏßPF2µÄбÂÊΪk2£»
£¨i£©ÇóÖ¤£ºk1k2=-$\frac{1}{2}$    
£¨ii£©Çó|MN|?|EF|µÄÈ¡Öµ·¶Î§£®

·ÖÎö £¨1£©ÍÖÔ²C4µÄ·½³ÌΪ£º$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}$=4£¬¼´£º$\frac{{x}^{2}}{4{a}^{2}}+\frac{{y}^{2}}{4{b}^{2}}$=1£®²»·ÁÉèc2=a2-b2£¬ÔòF2£¨2c£¬0£©£®ÓÉ$\overrightarrow{A{F}_{2}}$?$\overrightarrow{{F}_{1}{F}_{2}}$=0£¬¿ÉµÃ$\overrightarrow{A{F}_{2}}$¡Í$\overrightarrow{{F}_{1}{F}_{2}}$£®2c=2£¬$\frac{£¨2b£©^{2}}{2a}$=$\frac{2{b}^{2}}{a}$=$\sqrt{2}$£¬2b4=a2=b2+1£¬½â³ö¼´¿ÉµÃ³ö£®
£¨2£©£¨i£©ÍÖÔ²C2µÄ·½³ÌΪ£º$\frac{{x}^{2}}{2}$+y2=2 ¼´£º$\frac{{x}^{2}}{4}$+$\frac{{y}^{2}}{2}$=1£®ÍÖÔ²C4µÄ·½³ÌΪ£º$\frac{{x}^{2}}{8}+\frac{{y}^{2}}{4}$=1£®ÉèP£¨x0£¬y0£©£¬ÓÉPÔÚÍÖÔ²C2ÉÏ£¬¿ÉµÃy02=$\frac{1}{2}$£¨4-x02£©£®ÔÙÀûÓÃбÂʼÆË㹫ʽ¼´¿ÉÖ¤Ã÷k1k2Ϊ¶¨Öµ£®
£¨ii£©ÉèÖ±ÏßPF1µÄ·½³ÌΪ£ºy=k1£¨x+2£©Ö±ÏßPF2µÄ·½³ÌΪ£ºy=k2£¨x-2£©£¬ÓëÍÖÔ²·½³ÌÁªÁ¢ÏûÔªÕûÀíµÃ£º£¨2k12+1£©x2+8k1x+8k12-8=0£¬ÉèE£¨x1£¬y1£©£¬F£¨x2£¬y2£©£¬ÀûÓøùÓëϵÊýµÄ¹Øϵ¿ÉµÃ|EF|=$\sqrt{1+{k}_{1}^{2}}$$•\sqrt{£¨{x}_{1}+{x}_{2}£©^{2}-4{x}_{1}{x}_{2}}$£¬|MN|£®ÀûÓã¨i£©µÄ½áÂÛ´úÈë|EF|?|MN|£¬»¯¼ò¼´¿ÉÖ¤Ã÷£®

½â´ð ½â£º£¨1£©½â£ºÍÖÔ²C4µÄ·½³ÌΪ£º$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}$=4£¬¼´£º$\frac{{x}^{2}}{4{a}^{2}}+\frac{{y}^{2}}{4{b}^{2}}$=1£®
²»·ÁÉèc2=a2-b2   ÔòF2£¨2c£¬0£©£®
¡ß$\overrightarrow{A{F}_{2}}$?$\overrightarrow{{F}_{1}{F}_{2}}$=0£¬¡à$\overrightarrow{A{F}_{2}}$¡Í$\overrightarrow{{F}_{1}{F}_{2}}$£®
ÓÚÊÇ2c=2£¬$\frac{£¨2b£©^{2}}{2a}$=$\frac{2{b}^{2}}{a}$=$\sqrt{2}$£¬2b4=a2=b2+1£¬
¡à2b4-b2-1=0£¬
 £¨2b2+1£©£¨b2-1£©=0£¬
¡àb2=1£¬a2=2£®
¡àÍÖÔ²CnµÄ·½³ÌΪ£º$\frac{x2}{2}$+y2=n£®
¡àe2=$\frac{2{n}^{2}-{n}^{2}}{2{n}^{2}}$=$\frac{1}{2}$£¬¡àe=$\frac{\sqrt{2}}{2}$£®
ÍÖÔ²C1µÄ·½³ÌΪ£º$\frac{x2}{2}$+y2=1£®
£¨2£©£¨i£©Ö¤Ã÷£ºÍÖÔ²C2µÄ·½³ÌΪ£º$\frac{{x}^{2}}{2}$+y2=2   ¼´£º$\frac{{x}^{2}}{4}$+$\frac{{y}^{2}}{2}$=1£®
ÍÖÔ²C4µÄ·½³ÌΪ£º$\frac{{x}^{2}}{2}$+y2=4   ¼´£º$\frac{{x}^{2}}{8}+\frac{{y}^{2}}{4}$=1£®
¡àF1£¨-2£¬0£©£¬F2£¨2£¬0£©£¬ÉèP£¨x0£¬y0£©£¬
¡ßPÔÚÍÖÔ²C2ÉÏ£¬¡à$\frac{{x}_{0}^{2}}{4}+\frac{{y}_{0}^{2}}{2}$=1£¬¼´y02=$\frac{1}{2}$£¨4-x02£©£®
¡àk1k2=$\frac{{y}_{0}}{{x}_{0}+2}$•$\frac{{y}_{0}}{{x}_{0}-2}$=$\frac{{y}_{0}^{2}}{{x}_{0}^{2}-4}$=$\frac{\frac{1}{2}£¨4-{x}_{0}^{2}£©}{{x}_{0}^{2}-4}$=-$\frac{1}{2}$£®
£¨ii£©ÉèÖ±ÏßPF1µÄ·½³ÌΪ£ºy=k1£¨x+2£©Ö±ÏßPF2µÄ·½³ÌΪ£ºy=k2£¨x-2£©£¬
ÁªÁ¢·½³Ì×飺$\left\{\begin{array}{l}{\frac{{x}^{2}}{8}+\frac{{y}^{2}}{4}=1}\\{y={k}_{1}£¨x+2£©}\end{array}\right.$  ÏûÔªÕûÀíµÃ£º£¨2k12+1£©x2+8k1x+8k12-8=0¡­¢Ù
ÉèE£¨x1£¬y1£©£¬F£¨x2£¬y2£©£¬Ôòx1£¬x2ÊÇ·½³Ì¢ÙµÄÁ½¸ö½â£¬ÓÉΤ´ï¶¨ÀíµÃ£º
x1+x2=-$\frac{8{k}_{1}}{2{k}_{1}^{2}+1}$£¬x1x2=$\frac{8{k}_{1}^{2}-8}{2{k}_{1}^{2}+1}$£®
¡à|EF|=$\sqrt{1+{k}_{1}^{2}}$$•\sqrt{£¨{x}_{1}+{x}_{2}£©^{2}-4{x}_{1}{x}_{2}}$=$\frac{4\sqrt{2}£¨1+{k}_{1}^{2}£©}{2{k}_{1}^{2}+1}$£®
ͬÀí£º|MN|=$\frac{4\sqrt{2}£¨1+{k}_{2}^{2}£©}{2{k}_{2}^{2}+1}$£®
¡à|EF|?|MN|=$\frac{4\sqrt{2}£¨1+{k}_{1}^{2}£©}{2{k}_{1}^{2}+1}$•$\frac{4\sqrt{2}£¨1+{k}_{2}^{2}£©}{2{k}_{2}^{2}+1}$=32¡Á$\frac{{k}_{1}^{2}{k}_{2}^{2}+{k}_{1}^{2}+{k}_{2}^{2}+1}{4{k}_{1}^{2}{k}_{2}^{2}+2{k}_{1}^{2}+2{k}_{2}^{2}+1}$=32¡Á$\frac{£¨-\frac{1}{2}£©^{2}+{k}_{1}^{2}+{k}_{2}^{2}+1}{4¡Á£¨-\frac{1}{2}£©^{2}+2{k}_{1}^{2}+2{k}_{2}^{2}+1}$=$16+\frac{4}{{k}_{1}^{2}+{k}_{2}^{2}+1}$
=16+$\frac{4}{{k}_{1}^{2}+\frac{1}{4{k}_{1}^{2}}+1}$¡Ü18£¬
ÓÖ|EF|?|MN|£¾0£®
¡à|EF|?|MN|¡Ê£¨16£¬18]£®

µãÆÀ ±¾Ì⿼²éÁËÍÖÔ²µÄ±ê×¼·½³Ì¼°ÆäÐÔÖÊ¡¢Ö±ÏßÓëÍÖÔ²ÏཻÏÒ³¤ÎÊÌâ¡¢Ò»Ôª¶þ´Î·½³ÌµÄ¸ùÓëϵÊýµÄ¹Øϵ¡¢»ù±¾²»µÈʽµÄÐÔÖÊ£¬¿¼²éÁËÍÆÀíÄÜÁ¦Óë¼ÆËãÄÜÁ¦£¬ÊôÓÚÄÑÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

11£®É躯Êýf£¨x£©=$\left\{\begin{array}{l}{x-2£¬x¡Ý1}\\{2£¬x£¼1}\end{array}\right.$£¬ÔòÂú×ãxf£¨x-1£©¡Ý10µÄxÈ¡Öµ·¶Î§Îª[5£¬+¡Þ£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

12£®¡°x£¾-2¡±ÊÇ¡°£¨x+2£©£¨x-3£©£¼0¡±µÄ£¨¡¡¡¡£©
A£®³ä·Ö²»±ØÒªÌõ¼þB£®±ØÒª²»³ä·ÖÌõ¼þ
C£®³ä·Ö±ØÒªÌõ¼þD£®¼È²»³ä·ÖÒ²²»±ØÒªÌõ¼þ

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

9£®ÔÚ¿Õ¼äÖУ¬ÏÂÁÐÃüÌâÖв»ÕýÈ·µÄÊÇ£¨¡¡¡¡£©
A£®ÈôÁ½¸öƽÃæÓÐÒ»¸ö¹«¹²µã£¬ÔòËüÃÇÓÐÎÞÊý¸ö¹«¹²µã
B£®ÈÎÒâÁ½ÌõÖ±ÏßÄÜÈ·¶¨Ò»¸öƽÃæ
C£®ÈôµãA¼ÈÔÚƽÃæ¦ÁÄÚ£¬ÓÖÔÚƽÃæ¦ÂÄÚ£¬Ôò¦ÁÓë¦ÂÏཻÓÚÖ±Ïßb£¬ÇÒµãAÔÚÖ±ÏßbÉÏ
D£®ÈôÒÑÖªËĸöµã²»¹²Ã棬ÔòÆäÖÐÈÎÒâÈýµã²»¹²Ïß

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

16£®ÔÚ¡÷ABCÖУ¬½ÇA£¬B£¬CËù¶ÔµÄ±ß·Ö±ðΪa£¬b£¬c£¬ÇÒ2bcosC-3ccosB=a£¬Ôòtan£¨B-C£©µÄ×î´óֵΪ$\frac{3}{4}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

6£®ÒÑÖªÅ×ÎïÏßCµÄ¶¥µãÔÚÔ­µã£¬½¹µãΪF£¨-3£¬0£©£¬CÉÏÒ»µãPµ½½¹µãFµÄ¾àÀëΪ9£¬ÔòµãPµÄÒ»¸ö×ø±êΪ£¨¡¡¡¡£©
A£®£¨-3£¬6£©B£®£¨-3£¬6$\sqrt{2}$£©C£®£¨-6£¬6£©D£®£¨-6£¬6$\sqrt{2}$£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

13£®ÃüÌâp£º¡°?x¡ÊR£¬x2+2£¼0¡±£¬Ôò©VpΪ£¨¡¡¡¡£©
A£®?x¡ÊR£¬x2+2¡Ý0B£®?x∉R£¬x2+2£¼0C£®?x¡ÊR£¬x2+2¡Ý0D£®?x¡ÊR£¬x2+2£¾0

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

10£®Èçͼ£¬Ä³¼¸ºÎÌåµÄÖ÷ÊÓͼºÍ×óÊÓͼÊÇÈ«µÈµÄµÈÑüÖ±½ÇÈý½ÇÐΣ¬¸©ÊÓͼÊDZ߳¤Îª2µÄÕý·½ÐΣ¬ÄÇôËüµÄÌå»ýΪ£¨¡¡¡¡£©
A£®$\frac{16}{3}$B£®4C£®$\frac{8}{3}$D£®$\frac{4}{3}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

1£®ÒÑÖªÇãб½ÇΪ60¡ãµÄÖ±Ïßl¹ýµã£¨0£¬-2$\sqrt{3}$£©ºÍÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÓÒ½¹µã£¬ÇÒÍÖÔ²µÄÀëÐÄÂÊΪ$\frac{\sqrt{6}}{3}$£®
£¨¢ñ£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨¢ò£©¹ý£¨-3£¬0£©µãµÄÖ±ÏßlÓëÍÖÔ²ÏཻÓÚA£¬BÁ½µã£¬ÈôÒÔÏ߶ÎA£¬BΪֱ¾¶µÄÔ²¹ýÍÖÔ²µÄ×󽹵㣬ÇóÖ±ÏßlµÄ·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸