10£®ÒÑÖªÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÀëÐÄÂÊΪ$\frac{\sqrt{6}}{3}$£¬µãP£¨$\frac{\sqrt{3}}{2}$£¬$\frac{\sqrt{3}}{2}$£©ÔÚCÉÏ
£¨¢ñ£©ÇóÍÖÔ²CµÄ·½³Ì
£¨¢ò£©ÓëÔ²x2+y2=b2ÏàÇеÄÖ±ÏßlÓëC½»ÓÚ²»Í¬µÄÁ½µãM£¬N£¬µ±|MN|=$\sqrt{3}$ʱ£¬ÇóÖ±ÏßlµÄбÂÊ£®

·ÖÎö £¨¢ñ£©ÓÉÌâÒâµÃµ½a£¬bµÄ¹ØÏµ£¬µÃµ½ÍÖÔ²CµÄ·½³ÌΪ$\frac{{x}^{2}}{3{b}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$£®°ÑµãP£¨$\frac{\sqrt{3}}{2}$£¬$\frac{\sqrt{3}}{2}$£©´úÈëÇóµÃb2=1£¬½ø¶øµÃa2=3£¬ÔòÍÖÔ²·½³Ì¿ÉÇó£»
£¨¢ò£©ÈôÖ±ÏßlµÄбÂʲ»´æÔÚʱ£¬²»·ÁÉèlµÄ·½³ÌΪx=1£¬´úÈë$\frac{{x}^{2}}{3}+{y}^{2}=1$£¬ÇóµÃ|MN|=$\frac{2\sqrt{6}}{3}$¡Ù$\sqrt{3}$£¬²»ºÏÌâÒ⣮ÈôÖ±ÏßlµÄбÂÊ´æÔÚʱ£¬ÉèlµÄ·½³ÌΪy=kx+m£¬ÓÉÌâÒ⣬ÓÐ$\frac{|m|}{\sqrt{1+{k}^{2}}}=1$µÃµ½mÓëkµÄ¹ØÏµ£®ÁªÁ¢Ö±Ïß·½³ÌºÍÍÖÔ²·½³Ì£¬ÓÉÏÒ³¤¹«Ê½µÃµ½|MN|=$\frac{2\sqrt{6}|k|\sqrt{1+{k}^{2}}}{1+3{k}^{2}}=\sqrt{3}$£¬½â·½³ÌÇóµÃkµÄÖµ£®

½â´ð ½â£º£¨¢ñ£©ÓÉÌâÒ⣬ÓÐe2=1-$\frac{{b}^{2}}{{a}^{2}}$=$\frac{2}{3}$£¬µÃa2=3b2£¬¼´ÍÖÔ²CµÄ·½³ÌΪ$\frac{{x}^{2}}{3{b}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$£®
¡ßµãPÔÚCÉÏ£¬½«µãP£¨$\frac{\sqrt{3}}{2}$£¬$\frac{\sqrt{3}}{2}$£©µÄ×ø±ê´úÈ룬µÃb2=1£¬½ø¶øa2=3£¬
¡àÍÖÔ²CµÄ·½³ÌΪ$\frac{{x}^{2}}{3}+{y}^{2}=1$£»
£¨¢ò£©µ±Ö±ÏßlµÄбÂʲ»´æÔÚʱ£¬²»·ÁÉèlµÄ·½³ÌΪx=1£¬´úÈë$\frac{{x}^{2}}{3}+{y}^{2}=1$£¬
µÃM£¨1£¬$\frac{\sqrt{6}}{3}$£©£¬N£¨1£¬-$\frac{\sqrt{6}}{3}$£©£¬|MN|=$\frac{2\sqrt{6}}{3}$¡Ù$\sqrt{3}$£¬²»ºÏÌâÒ⣮
µ±Ö±ÏßlµÄбÂÊ´æÔÚʱ£¬ÉèlµÄ·½³ÌΪy=kx+m£¬
ÓÉÌâÒ⣬ÓÐ$\frac{|m|}{\sqrt{1+{k}^{2}}}=1$£¬¼´m2=k2+1£®
½«y=kx+m´úÈë$\frac{{x}^{2}}{3}+{y}^{2}=1$£¬µÃ£¨1+3k2£©x2+6kmx+3m2-3=0£¬
ÉèM£¨x1£¬y1£©£¬N£¨x2£¬y2£©£¬Ôòx1+x2=$\frac{-6km}{1+3{k}^{2}}$£¬x1x2=$\frac{3{m}^{2}-3}{1+3{k}^{2}}$£¬
¡à|MN|=$\sqrt{1+{k}^{2}}|{x}_{1}-{x}_{2}|=\sqrt{1+{k}^{2}}\sqrt{£¨{x}_{1}+{x}_{2}£©^{2}-4{x}_{1}{x}_{2}}$=$\sqrt{1+{k}^{2}}$¡Á$\frac{2\sqrt{3£¨3{k}^{2}+1-{m}^{2}£©}}{1+3{k}^{2}}$
=$\frac{2\sqrt{6}|k|\sqrt{1+{k}^{2}}}{1+3{k}^{2}}=\sqrt{3}$£¬ÕûÀí£¬µÃk4-2k2+1=0£¬½âµÃk2=1£¬k=¡À1£®
×ÛÉÏ£¬¿ÉÖªÖ±ÏßlµÄбÂÊΪ¡À1£®

µãÆÀ ±¾Ì⿼²éÁËÍÖÔ²·½³ÌµÄÇ󷨣¬¿¼²éÁËÖ±ÏߺÍÔ²×¶ÇúÏßµÄλÖùØÏµ£¬ÑµÁ·ÁËÏÒ³¤¹«Ê½µÄÓ¦Óã¬ÊÇÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®ÉèSÊÇÕûÊý¼¯ZµÄ·Ç¿Õ×Ó¼¯£¬Èç¹û?a£¬b¡ÊZ£¬¶¼ÓÐa2-b2¡ÊS£¬Ôò³ÆSÊÇÒ»¸öºÃ¼¯£¬ÒÑÖªSÊÇÒ»¸ö¡°ºÃ¼¯¡±£¬ÏÂÃæÃüÌâΪ¼ÙÃüÌâµÄÊÇ£¨¡¡¡¡£©
A£®Ò»ÇÐÆæÊý¶¼ÊôÓÚSB£®Å¼Êý4k-2£¨k¡ÊZ£©¶¼²»ÊôÓÚS
C£®Èôx£¬y¡ÊS£¬Ôòxy¡ÊSD£®Èôx£¬yÊôÓÚS£¬Ôòx+y¡ÊS

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

1£®Èçͼ£¬ÒÑÖª¡÷ABC£¬A£¨7£¬8£©£¬B£¨3£¬5£©£¬C£¨4£¬3£©£¬M£¬N£¬D·Ö±ðÊÇAB£¬AC£¬BCµÄÖе㣬ÇÒMNÓëAD½»ÓÚF£®
£¨1£©Çó£º$\overrightarrow{DF}$£®
£¨2£©Çó¡ÏBACµÄÓàÏÒÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

18£®ÒÑÖªÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©×ó½¹µãΪF£¨-1£¬0£©£¬MΪÓÒ×¼Ïßx=4ÉϵÄÒ»¶¯µã£¨²»ÔÚxÖáÉÏ£©£¬Ïß¶ÎFM½»ÍÖÔ²ÓÚµãP£¬MAÓëÍÖÔ²µÄÁíÒ»½»µãΪQ£®
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨2£©ÉèÖ±ÏßPFµÄбÂÊΪk1£¬Ö±ÏßPAµÄбÂÊΪk2£¬Çók1k2µÄȡֵ·¶Î§£»
£¨3£©µ±Ö±ÏßOQ´¹Ö±ÓÚÖ±ÏßMFʱ£¬ÇóµãPµÄºá×ø±ê£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

5£®º¯Êýf£¨x£©=sinx•ln£¨x+1£©µÄͼÏó´óÖÂΪ£¨¡¡¡¡£©
A£®B£®C£®D£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

15£®¹ýµãA£¨2£¬-4£©ÇÒÓëÖ±Ïß2x-y+3=0ƽÐеÄÖ±Ïß·½³ÌΪ£¨¡¡¡¡£©
A£®x+2y-8=0B£®2x-y-8=0C£®x+2y-4=0D£®2x-y=0

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

2£®ÒÑÖªÒ»¸öÇòÓëÒ»¸öÕýÈýÀâÖùµÄÈý¸ö²àÃæºÍÁ½¸öµ×Ãæ¶¼ÏàÇУ¬Õâ¸öÇòµÄ±íÃæ»ýÊÇ4¦Ð£¬ÔòÕâ¸öÈýÀâÖùµÄÌå»ýÊÇ$6\sqrt{3}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®ÒÑÖªº¯Êýf£¨n£©=logn+1£¨n+2£©£¨n¡ÊN*£©£¬¶¨Òåʹf£¨1£©•f£¨2£©¡­f£¨k£©ÎªÕûÊýµÄÊýk£¨k¡ÊN*£©½Ð×öÆóÅÎÊý£¬ÔòÔÚÇø¼ä[1£¬50]ÄÚÕâÑùµÄÆóÅÎÊý¹²ÓУ¨¡¡¡¡£©¸ö£®
A£®2B£®3C£®4D£®5

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

20£®ÒÑÖªÊýÁÐ{an}Âú×ãan+12-2an+1an-3an2=0£¬a2=1£¬ÇÒan+1£¾an£¬n¡ÊN*£¬Ôò{an}µÄǰ10ÏîºÍµÈÓÚ£¨¡¡¡¡£©
A£®6£¨310-1£©B£®$\frac{1}{6}$£¨310-1£©C£®6£¨1-310£©D£®$\frac{1}{6}$£¨1-310£©

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸