10£®Èçͼ£¬ÔÚÆ½ÃæÖ±½Ç×ø±êϵxOyÖУ¬ÒÑÖªÍÖÔ²E£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÀëÐÄÂÊΪ$\frac{\sqrt{2}}{2}$£¬µãA£¨$\frac{1}{3}$£¬$\frac{2}{3}$£©ÔÚÍÖÔ²EÉÏ£¬ÉäÏßAOÓëÍÖÔ²EµÄÁíÒ»½»µãΪB£¬µãP£¨-4t£¬t£©ÔÚÍÖÔ²EÄÚ²¿£¬ÉäÏßAP¡¢BPÓëÍÖÔ²EµÄÁíÒ»½»µã·Ö±ðΪC£¬D£®
£¨1£©ÇóÍÖÔ²EµÄ·½³Ì£»
£¨2£©ÇóÖ¤£ºÖ±ÏßCDµÄбÂÊΪ¶¨Öµ£®

·ÖÎö £¨1£©½«µãA´úÈëÍÖÔ²·½³Ì£¬e=$\frac{c}{a}=\sqrt{1-\frac{{b}^{2}}{{a}^{2}}}=\frac{\sqrt{2}}{2}$£¬ÁªÁ¢ÇóµÃaºÍbµÄÖµ£¬ÇóµÃÍÖÔ²·½³Ì£»
£¨2£©¸ù¾Ý¶Ô³ÆÐÔÇóµÃBµã×ø±ê£¬$\overrightarrow{AP}$=${¦Ë}_{1}\overrightarrow{PC}$£¬$\overrightarrow{BP}={¦Ë}_{2}\overrightarrow{PD}$£¬ÇóµÃx1ºÍy1£¬´úÈëÍÖÔ²·½³Ì£¬ÇóµÃ$£¨{¦Ë}_{1}+1£©•18{t}^{2}={¦Ë}_{1}-1$£¬Í¬ÀíÇóµÃ£¨¦Ë2+1£©•18t2=¦Ë2-1£¬Á½Ê½Ïà¼õÇóµÃ¦Ë1=¦Ë2£¬Òò´Ë¿ÉÖ¤Ã÷CD¡ÎAB£¬½øÒ»²½Çó³öÖ±ÏßABµÄбÂÊ£¬Ôò½áÂÛ¿ÉÖ¤£®

½â´ð £¨1£©½â£º½«µãA´úÈëÍÖÔ²·½³ÌµÃ£º$\frac{£¨\frac{1}{3}£©^{2}}{{a}^{2}}+\frac{£¨\frac{2}{3}£©^{2}}{{b}^{2}}=1$£¬ÇÒe=$\frac{c}{a}=\sqrt{1-\frac{{b}^{2}}{{a}^{2}}}=\frac{\sqrt{2}}{2}$£¬
½âµÃ£ºa2=1£¬${b}^{2}=\frac{1}{2}$£¬
¡àÍÖÔ²EµÄ·½³ÌΪ£ºx2+2y2=1£»
£¨2£©Ö¤Ã÷£º¡ßA£¨$\frac{1}{3}$£¬$\frac{2}{3}$£©£¬¡àB£¨-$\frac{1}{3}$£¬-$\frac{2}{3}$£©£¬
ÉèC£¨x1£¬y1£©£¬D£¨x2£¬y2£©£¬$\overrightarrow{AP}$=${¦Ë}_{1}\overrightarrow{PC}$£¬$\overrightarrow{BP}={¦Ë}_{2}\overrightarrow{PD}$£¬ÆäÖУº¦Ë1£¬¦Ë2¡Ê£¨0£¬1£©£¬
Ôò$\left\{\begin{array}{l}{{x}_{1}=\frac{£¨{¦Ë}_{1}+1£©£¨-4t£©-\frac{1}{3}}{{¦Ë}_{1}}}\\{{y}_{1}=\frac{£¨{¦Ë}_{1}+1£©t-\frac{2}{3}}{{¦Ë}_{1}}}\end{array}\right.$£¬´úÈëÍÖÔ²·½³Ì²¢ÕûÀíµÃ£¬$£¨{¦Ë}_{1}+1£©•18{t}^{2}={¦Ë}_{1}-1$£¬
ͬÀíµÃ£¬£¨¦Ë2+1£©•18t2=¦Ë2-1£¬
Á½Ê½Ïà¼õµÃ£º£¨¦Ë1-¦Ë2£©•£¨18t2-1£©=0£®
¡ßµãP£¨-4t£¬t£©ÔÚÍÖÔ²EÄÚ²¿£¬
¡à18t2£¼1£¬
¡à¦Ë1=¦Ë2£¬
¡àCD¡ÎAB£®
ÓÖ${k}_{AB}=\frac{-\frac{2}{3}-\frac{2}{3}}{-\frac{1}{3}-\frac{1}{3}}=2$£®
¡àÖ±ÏßCDµÄбÂÊΪ¶¨Öµ£®

µãÆÀ ±¾Ì⿼²éÇóÍÖÔ²µÄ·½³Ì£¬ÀûÓÃÏòÁ¿¹²Ïß¶¨ÀíÖ¤Ã÷Á½Ö±Ï߯½ÐУ¬µãµÄ¶Ô³ÆÐÔ£¬¿¼²é×ۺϷÖÎöÎÊÌâ¼°½â¾öÎÊÌâµÄÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º2017½ì°²»ÕºÏ·ÊÒ»ÖиßÈýÉÏѧÆÚÔ¿¼Ò»Êýѧ£¨Àí£©ÊÔ¾í£¨½âÎö°æ£© ÌâÐÍ£º½â´ðÌâ

ÒÑÖª£¬£¬ÈôÊǵijä·Ö¶ø²»±ØÒªÌõ¼þ£¬ÇóʵÊýµÄȡֵ·¶Î§.

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º2016-2017ѧÄêºÓ±±Õý¶¨ÖÐѧ¸ß¶þÉÏÔ¿¼Ò»Êýѧ£¨Àí£©ÊÔ¾í£¨½âÎö°æ£© ÌâÐÍ£º½â´ðÌâ

ij¹«Ë¾2016ÄêǰÈý¸öÔµÄÀûÈ󣨵¥Î»£º°ÙÍòÔª£©ÈçÏ£º

£¨1£©ÇóÀûÈó¹ØÓÚÔ·ݵÄÏßÐԻع鷽³Ì£»

£¨2£©ÊÔÓã¨1£©ÖÐÇóµÃµÄ»Ø¹é·½³ÌÔ¤²â4ÔºÍ5ÔµÄÀûÈó£»

£¨3£©ÊÔÓã¨1£©ÖÐÇóµÃµÄ»Ø¹é·½³ÌÔ¤²â¸Ã¹«Ë¾2016Äê´Ó¼¸Ô·ݿªÊ¼ÀûÈ󳬹ý1000Íò£¿

Ïà¹Ø¹«Ê½£º£¬£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º2016-2017ѧÄêºÓ±±Õý¶¨ÖÐѧ¸ß¶þÉÏÔ¿¼Ò»Êýѧ£¨Àí£©ÊÔ¾í£¨½âÎö°æ£© ÌâÐÍ£ºÑ¡ÔñÌâ

ÔËÐÐÏÂÃæµÄ³ÌÐò£¬Èô£¬ÔòÊä³öµÄµÈÓÚ£¨ £©

A£®9 B£®7 C£®13 D£®11

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

5£®Èçͼ£¬ÔÚ¶àÃæÌåABCDEÖУ¬DB¡ÍÆ½ÃæABC£¬AE¡ÎDB£¬ÇÒ¡÷ABCÊDZ߳¤Îª2µÄµÈ±ßÈý½ÇÐΣ¬2AE=BD=2£®
£¨¢ñ£©ÈôFÊÇÏß¶ÎCDµÄÖе㣬֤Ã÷£ºEF¡ÍÃæDBC£»
£¨¢ò£©Çó¶þÃæ½ÇD-EC-BµÄÆ½Ãæ½ÇµÄÓàÏÒÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

15£®ÒÑÖªÏòÁ¿$\overrightarrow a$£¬$\overrightarrow b$µÄ¼Ð½ÇΪ60¡ã£¬ÇÒ|$\overrightarrow a$|=1£¬|$\overrightarrow{b}$|=2£¬Ôò|2$\overrightarrow a$+$\overrightarrow{b}$|=£¨¡¡¡¡£©
A£®$\sqrt{3}$B£®$\sqrt{5}$C£®$2\sqrt{2}$D£®$2\sqrt{3}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

2£®ÉèF1£¬F2·Ö±ðÊÇÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$£¨a£¾b£¾0£©µÄ×óÓÒ½¹µã£¬MÊÇCÉÏÒ»µãÇÒMF2ÓëxÖá´¹Ö±£¬Ö±ÏßMF1ÓëCµÄÁíÒ»¸ö½»µãΪN£®
£¨1£©ÈôÖ±ÏßMNµÄбÂÊΪ$\frac{3}{4}$£¬ÇóCµÄÀëÐÄÂÊ£»
£¨2£©ÈôÖ±ÏßMNÔÚyÖáÉϵĽؾàΪ2£¬ÇÒ|MN|=5|F1N|£¬ÇóÍÖÔ²±ê×¼·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

18£®Èçͼ£¬ËÄÀâ×¶P-ABCDÖУ¬µ×ÃæABCDÊǾØÐΣ¬PA¡ÍÆ½ÃæABCD£¬PA=AB=1£¬BC=2£¬EΪPDµÄÖеã

£¨1£©ÇóÒìÃæÖ±ÏßPAÓëCEËù³É½ÇµÄ´óС£»
£¨2£©ÇóÈýÀâ×¶A-CDEµÄÌå»ý£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

18£®¶¨»ý·Ö${¡Ò}_{0}^{¦Ð}$|sinx-cosx|dxµÄÖµÊÇ£¨¡¡¡¡£©
A£®2+$\sqrt{2}$B£®2-$\sqrt{2}$C£®2D£®2$\sqrt{2}$

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸