8£®ÒÑÖªÍÖÔ²E£º$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1£¨a£¾0£¬b£¾0£©$µÄÓÒ½¹µãF£¨1£¬0£©£¬³¤ÖáµÄ×ó¡¢ÓҶ˵ã·Ö±ðΪA1£¬A2£»ÇÒ$\overrightarrow{F{A_1}}•\overrightarrow{F{A_2}}=-1$£®
£¨1£©ÇóÍÖÔ²EµÄ·½³Ì£»
£¨2£©ÒÑÖªµãB£¨0£¬-1£©£¬¾­¹ýµã£¨1£¬1£©ÇÒбÂÊΪkµÄÖ±ÏßÓëÍÖÔ²E½»ÓÚ²»Í¬µÄÁ½P¡¢Qµã£¨¾ùÒìÓÚµãB£©£¬Ö¤Ã÷£ºÖ±ÏßBPÓëBQµÄбÂÊÖ®ºÍΪ¶¨Öµ£®

·ÖÎö £¨1£©ÉèA1£¨-a£¬0£©£¬A2£¨a£¬0£©£¬Ôò$\overrightarrow{F{A_1}}=£¨-a-1£¬0£©$£¬$\overrightarrow{F{A_2}}=£¨a-1£¬0£©$£¬ÀûÓÃ$\overrightarrow{F{A_1}}•\overrightarrow{F{A_2}}=-1$£®Çó³öa£¬Çó³öb£¬¼´¿ÉµÃµ½ÍÖÔ²·½³Ì£®
£¨2£©Ö±ÏßPQµÄ·½³ÌΪy=k£¨x-1£©+1£¨k¡Ù2£©£¬´úÈë$\frac{x^2}{2}+{y^2}=1$£¬ÏûÈ¥y£¬ÉèP£¨x1£¬y1£©£¬Q£¨x2£¬y2£©£¬x1x2¡Ù0ÀûÓÃΤ´ï¶¨Àí£¬Çó³öÖ±ÏßBPÓëBQµÄбÂÊÖ®ºÍ£¬»¯¼òÇó½â¼´¿É£®

½â´ð £¨±¾ÌâÂú·Ö12·Ö£©
£¨1£©ÉèA1£¨-a£¬0£©£¬A2£¨a£¬0£©£¬Ôò$\overrightarrow{F{A_1}}=£¨-a-1£¬0£©$£¬$\overrightarrow{F{A_2}}=£¨a-1£¬0£©$£¬
ÓÉ$\overrightarrow{F{A_1}}•\overrightarrow{F{A_2}}=-1$£¬µÃ1-a2=-1£¬ËùÒÔa2=2£¬ÍÖÔ²E£º$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1£¨a£¾0£¬b£¾0£©$µÄÓÒ½¹µãF£¨1£¬0£©£¬¿ÉµÃc=1£¬Ôòb2=1£®
ËùÒÔÍÖÔ²EµÄ·½³ÌΪ$\frac{x^2}{2}+{y^2}=1$£®
£¨2£©Ö¤Ã÷£ºÓÉÌâÉèÖª£¬Ö±ÏßPQµÄ·½³ÌΪy=k£¨x-1£©+1£¨k¡Ù2£©£¬
´úÈë$\frac{x^2}{2}+{y^2}=1$µÃ£¨1+2k2£©x2-4k£¨k-1£©x+2k£¨k-2£©=0£¬
ÓÉÒÑÖª¡÷£¾0  ÉèP£¨x1£¬y1£©£¬Q£¨x2£¬y2£©£¬x1x2¡Ù0£¬
Ôò${x_1}+{x_2}=\frac{4k£¨k-1£©}{{1+2{k^2}}}$£¬${x_1}{x_2}=\frac{2k£¨k-2£©}{{1+2{k^2}}}$£¬
´Ó¶øµãÏßBP£¬BQµÄбÂÊÖ®ºÍ¡­£¨6·Ö£©
${k_{BP}}+{k_{BQ}}=\frac{{{y_1}+1}}{x_1}+\frac{{{y_2}+1}}{x_2}$=$\frac{{k{x_1}+2-k}}{x_1}+\frac{{k{x_2}+2-k}}{x_2}$=$2k+£¨2-k£©\frac{{{x_1}+{x_2}}}{{{x_1}{x_2}}}$
=$2k+£¨2-k£©•\frac{4k£¨k-1£©}{2k£¨k-2£©}=2k-2£¨k-1£©=2$£®
¹ÊÖ±ÏßBPÓëBQµÄбÂÊÖ®ºÍΪ¶¨Öµ£®¡­£¨12·Ö£©

µãÆÀ ±¾Ì⿼²éÍÖÔ²·½³ÌµÄÇ󷨣¬Ö±ÏßÓëÍÖÔ²µÄλÖùØϵµÄ×ÛºÏÓ¦Ó㬿¼²éת»¯Ë¼ÏëÒÔ¼°¼ÆËãÄÜÁ¦£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

18£®µÈ±ÈÊýÁÐ{an}µÄ¸÷Ïî¾ùΪÕýÊý£¬ÇÒa1+2a2=1£¬a32=4a2a6£®
£¨1£©ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨2£©Éèbn+2=3log2$\frac{1}{{a}_{n}}$£¬ÇóÊýÁÐ{anbn}µÄÇ°nÏîºÍ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®ÏÂÁк¯ÊýÖУ¬¼ÈÊÇżº¯ÊýÓÖÔÚÇø¼ä£¨0£¬1£©ÄÚµ¥µ÷µÝ¼õµÄÊÇ£¨¡¡¡¡£©
A£®y=x2B£®y=2xC£®y=cosxD£®y=lnx

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

16£®Ä³Ò»¼òµ¥¼¸ºÎÌåµÄÈýÊÓͼÈçͼ£¬Ôò¸Ã¼¸ºÎÌåµÄ±íÃæ»ýΪ£¨¡¡¡¡£©
A£®$2+\sqrt{5}$B£®5C£®$4+\sqrt{5}$D£®$2+2\sqrt{5}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

3£®ÔÚÈý½ÇÐÎABCÖУ¬½ÇA£¬B£¬CµÄ¶Ô±ß·Ö±ðΪa£¬b£¬c£¬ÒÑÖªa2+c2=4ac£¬Èý½ÇÐεÄÃæ»ýΪ$S=\frac{{\sqrt{3}}}{2}accosB$£¬ÔòsinAsinCµÄֵΪ$\frac{1}{4}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

3£®ÇúÏßy=$\frac{x}{2x-1}$Ôڵ㣨1£¬1£©´¦µÄÇÐÏß·½³ÌΪ£¨¡¡¡¡£©
A£®x-y-2=0B£®x+y-2=0C£®x+4y-5=0D£®x-4y-5=0

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

10£®ÒÑÖªµãPÊÇÍÖÔ²$\frac{x^2}{25}+\frac{y^2}{9}=1$ÉϵÄÒ»µã£¬ÇÒÒÔµãP¼°½¹µãF1£¬F2Ϊ¶¥µãµÄÈý½ÇÐεÄÃæ»ýµÈÓÚ4£¬µãPÔÚxÖáµÄÉÏ·½£¬ÇóµãPµÄ×ø±ê$£¨¡À\frac{{10\sqrt{2}}}{3}£¬1£©$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

7£®Éè¸÷Ïî¾ùΪÕýÊýµÄµÈ±ÈÊýÁÐ{an}ÖУ¬a1a3=64£¬a2+a5=72£®
£¨1£©ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨2£©£©Éè${b_n}=\frac{1}{{n{{log}_2}{a_n}}}$£¬SnÊÇÊýÁÐ{bn}µÄÇ°nÏîºÍ£¬²»µÈʽSn£¾loga£¨a-2£©¶ÔÈÎÒâÕýÕûÊýnºã³ÉÁ¢£¬ÇóʵÊýaµÄÈ¡Öµ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

8£®ÉèµãP£¨x£¬y£©ÔÚÍÖÔ²4x2+y2=4ÉÏ£¬Ôòx+yµÄ×î´óֵΪ£¨¡¡¡¡£©
A£®3B£®-3C£®4D£®$\sqrt{5}$

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸