6£®ÒÑÖªÍÖÔ²$C£º\frac{x^2}{a^2}+\frac{y^2}{b^2}=1£¨a£¾b£¾0£©$µÄÓÒ½¹µãÊÇÅ×ÎïÏßy2=4xµÄ½¹µã£¬ÒÔÔ­µãOΪԲÐÄ£¬ÍÖÔ²µÄ³¤°ëÖ᳤Ϊ°ë¾¶µÄÔ²ÓëÖ±Ïßx+y-2$\sqrt{2}$=0ÏàÇУ®
£¨1£©ÇóÍÖÔ²CµÄ±ê×¼·½³Ì£»
£¨2£©ÈôÖ±Ïßl£ºy=kx+mÓëÍÖÔ²CÏཻÓÚP£¬QÁ½µã£¬ÇÒ¡÷POQµÄÃæ»ýΪ¶¨Öµ$\sqrt{3}$£¬ÊÔÅжÏÖ±ÏßOPÓëOQµÄбÂÊÖ®»ýÊÇ·ñΪ¶¨Öµ£¿ÈôΪ¶¨Öµ£¬Çó³ö¶¨Öµ£»Èô²»Îª¶¨Öµ£¬Çë˵Ã÷ÀíÓÉ£®

·ÖÎö £¨1£©ÓÉÅ×ÎïÏß·½³ÌÇó³öÅ×ÎïÏߵĽ¹µã×ø±ê£¬¿ÉµÃcÖµ£¬ÔÙÓɵ㵽ֱÏߵľàÀ빫ʽÇóµÃa£¬ÓÉÒþº¬Ìõ¼þÇóµÃb£¬ÔòÍÖÔ²·½³Ì¿ÉÇó£»
£¨2£©ÁªÁ¢Ö±Ïß·½³ÌºÍÍÖÔ²·½³Ì£¬ÀûÓÃÏÒ³¤¹«Ê½ÇóµÃ|PQ|£¬ÔÙÓɵ㵽ֱÏߵľàÀ빫ʽÇóµÃOµ½Ö±ÏßlµÄ¾àÀ룬½áºÏ¡÷POQµÄÃæ»ýΪ¶¨Öµ$\sqrt{3}$ÇóµÃkÓëmµÄ¹ØÏµ£¬´úÈëбÂʹ«Ê½¿ÉµÃÖ±ÏßOPÓëOQµÄбÂÊÖ®»ýÊÇ·ñΪ¶¨Öµ£®

½â´ð ½â£º£¨1£©ÓÉy2=4x£¬µÃp=2£¬Ôò$\frac{p}{2}=1$£¬¡àc=1£¬
ÔÙÓɵ㵽ֱÏߵľàÀ빫ʽµÃa=$\frac{|-2\sqrt{2}|}{\sqrt{1+1}}=2$£¬
¡àb2=a2-c2=3£¬
¡àÍÖÔ²CµÄ±ê×¼·½³ÌΪ$\frac{x^2}{4}+\frac{y^2}{3}=1$£»
£¨2£©ÉèP£¨x1£¬y1£©£¬Q£¨x2£¬y2£©£¬
ÁªÁ¢$\left\{\begin{array}{l}{y=kx+m}\\{\frac{{x}^{2}}{4}+\frac{{y}^{2}}{3}=1}\end{array}\right.$£¬µÃ£¨3+4k2£©x2+8mkx+4£¨m2-3£©=0£¬
¡÷=64m2k2-16£¨3+4k2£©£¨m2-3£©£¾0£¬¼´3+4k2-m2£¾0£¬
${x_1}+{x_2}=-\frac{8mk}{{3+4{k^2}}}$£¬${x_1}{x_2}=\frac{{4£¨{m^2}-3£©}}{{3+4{k^2}}}$£¬
${y_1}{y_2}=£¨k{x_1}+m£©£¨k{x_2}+m£©={k^2}{x_1}{x_2}+mk£¨{x_1}+{x_2}£©+{m^2}=\frac{{3£¨{m^2}-4{k^2}£©}}{{3+4{k^2}}}$£¬
¡à$|PQ|=\sqrt{1+{k^2}}\sqrt{{{£¨{x_1}+{x_2}£©}^2}-4{x_1}{x_2}}=\frac{{\sqrt{1+{k^2}}\sqrt{48£¨4{k^2}-{m^2}+3£©}}}{{3+4{k^2}}}$£¬
Oµ½Ö±ÏßlµÄ¾àÀë$d=\frac{|m|}{{\sqrt{1+{k^2}}}}$£¬
¡à${S_{¡÷POQ}}=\sqrt{3}=\frac{1}{2}|PQ|\;•\;d=\frac{1}{2}\frac{{\sqrt{1+{k^2}}\sqrt{48£¨4{k^2}-{m^2}+3£©}}}{{3+4{k^2}}}\;•\;\frac{|m|}{{\sqrt{1+{k^2}}}}$£¬¿ÉµÃ2m2-4k2=3£®
Ôò${k_{OP}}\;•\;{k_{OQ}}=\frac{{{y_1}{y_2}}}{{{x_1}{x_2}}}=\frac{{3£¨{m^2}-4{k^2}£©}}{{4£¨{m^2}-3£©}}=-\frac{3}{4}$£¬
¡àkOP•kOQΪ¶¨Öµ$-\frac{3}{4}$£®

µãÆÀ ±¾Ì⿼²éÍÖÔ²µÄ¼òµ¥ÐÔÖÊ£¬¿¼²éÁËÖ±ÏßÓëÔ²×¶ÇúÏßλÖùØÏµµÄÓ¦Ó㬿¼²éµãµ½Ö±ÏߵľàÀ빫ʽ¼°ÏÒ³¤¹«Ê½µÄÓ¦Óã¬ÊôÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

16£®ÒÑÖª|$\overrightarrow{a}$|=2£¬|$\overrightarrow{b}$|=$\sqrt{3}$£¬$\overrightarrow{a}$£¬$\overrightarrow{b}$µÄ¼Ð½ÇΪ30¡ã£¬£¨$\overrightarrow{a}$+2$\overrightarrow{b}$£©¡Î£¨2$\overrightarrow{a}$+¦Ë$\overrightarrow{b}$£©£¬Ôò£¨£¨$\overrightarrow{a}$+¦Ë$\overrightarrow{b}$£©£©•£¨$\overrightarrow{a}$-$\overrightarrow{b}$£©=1£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

17£®º¯Êý$f£¨x£©=\left\{\begin{array}{l}sinx\\ 5\frac{|x|}{x}\end{array}\right.\begin{array}{l}£¬x£¾0\\ \\£¬x£¼0\end{array}$£¬Ôòf£¨-1£©=-5£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

14£®ÒÑÖªSnÊǵȲîÊýÁÐ{an}µÄǰnÏîºÍ£¬ÇÒS6£¾S7£¾S5£¬¸ø³öÏÂÁÐÎå¸öÃüÌ⣺
¢Ùd£¼0£»¢ÚSn£¾0£»¢ÛS12£¼0£»¢ÜÊýÁÐ{Sn}ÖеÄ×î´óÏîΪS11£»¢Ý|a6|£¾|a7|£®
ÆäÖÐÕýÈ·ÃüÌâµÄÐòºÅÊÇ£º¢Ù¢Ý£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

1£®ÈçͼËùʾµÄÊýÕóÖУ¬Ã¿ÐС¢Ã¿ÁеÄÈý¸öÊý¾ù³ÉµÈ²îÊýÁУ¬Èç¹ûÊýÕóÖÐËùÓÐÊýÖ®ºÍµÈÓÚ63£¬ÄÇôa52=£¨¡¡¡¡£©
$£¨{\begin{array}{l}{{a_{41}}}&{{a_{42}}}&{{a_{43}}}\\{{a_{51}}}&{{a_{52}}}&{{a_{53}}}\\{{a_{61}}}&{{a_{62}}}&{{a_{63}}}\end{array}}£©$£®
A£®2B£®8C£®7D£®4

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

11£®ÊýÁÐ{an}ÖУ¬an+2=an+1-an£¬a1=2£¬a2=5£¬Ôòa2013Ϊ£¨¡¡¡¡£©
A£®3B£®-2C£®5D£®-3

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

18£®ÒÑÖªº¯Êýf£¨x£©=sin£¨2x+¦Õ£©£¬ÆäÖÐ$\frac{¦Ð}{2}$£¼|¦Õ|£¼¦Ð£¬Èô$f£¨x£©¡Ü|f£¨\frac{¦Ð}{6}£©|$¶Ôx¡ÊRºã³ÉÁ¢£¬Ôòf£¨x£©µÄµÝÔöÇø¼äÊÇ£¨¡¡¡¡£©
A£®$[k¦Ð-\frac{¦Ð}{3}£¬k¦Ð+\frac{¦Ð}{6}]£¨k¡ÊZ£©$B£®$[k¦Ð£¬k¦Ð+\frac{¦Ð}{2}]£¨k¡ÊZ£©$C£®$[k¦Ð+\frac{¦Ð}{6}£¬k¦Ð+\frac{2¦Ð}{3}]£¨k¡ÊZ£©$D£®$[k¦Ð-\frac{¦Ð}{2}£¬k¦Ð]£¨k¡ÊZ£©$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

15£®ÏÂÁк¯ÊýÖÐÖÜÆÚΪ¦ÐµÄÊÇ£¨¡¡¡¡£©
A£®y=|sinx|B£®y=|cos2x|C£®y=tan2xD£®y=sin2x£¬x¡Ê£¨0£¬2¦Ð£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

16£®ÍÖÔ²C£º$\frac{x^2}{a^2}+\frac{y^2}{b^2}$=1£¨a£¾b£¾0£©µÄ×ó¡¢ÓÒ½¹µã·Ö±ðÊÇF1£¬F2£¬ÀëÐÄÂÊΪ$\frac{{\sqrt{3}}}{2}$£¬¹ýF1ÇÒ´¹Ö±ÓÚxÖáµÄÖ±Ïß±»ÍÖÔ²C½ØµÃµÄÏ߶γ¤Îª1£¬A£¬BΪÍÖÔ²CÉϵÄÁ½µã£¬OÎª×ø±êÔ­µã£¬ÉèÖ±ÏßOA£¬OB£¬ABµÄбÂÊ·Ö±ðΪk1£¬k2£¬k£®
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì
£¨2£©µ±k1k2-1=k1+k2ʱ£¬ÇókµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸