8£®ÒÑÖªÍÖÔ²C£º$\frac{x^2}{a^2}+\frac{y^2}{b^2}$=1£¨a£¾b£¾0£©¾­¹ýµã£¨0£¬$\sqrt{3}}$£©£¬ÀëÐÄÂÊΪ$\frac{1}{2}$£¬×ó£¬ÓÒ½¹µã·Ö±ðΪF1£¨-c£¬0£©£¬F2£¨c£¬0£©£®
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨2£©ÈôÖ±Ïßl£ºy=-$\frac{1}{2}$x+mÓëÍÖÔ²½»ÓÚA£¬BÁ½µã£¬ÓëÔ²x2+y2=c2½»ÓÚC£¬DÁ½µã£¬ÇÒÂú×㣺|AB|=$\frac{{5\sqrt{3}}}{4}$|CD|£¬ÇóÖ±ÏßlµÄ·½³Ì£®

·ÖÎö £¨1£©ÓÉÌâÒâ¿ÉµÃ£ºb=$\sqrt{3}$£¬$\frac{c}{a}$=$\frac{1}{2}$£¬a2=c2+b2£¬ÁªÁ¢½â³ö¼´¿ÉµÃ³ö£®
£¨2£©ÓÉ£¨1£©ÖªÔ²x2+y2=1£¬Ô²ÐÄ£¨0£¬0£©µ½lµÄ¾àÀë$d=\frac{2|m|}{{\sqrt{5}}}$£¼1£¬ÀûÓÃ|CD|=2$\sqrt{{r}^{2}-{d}^{2}}$£¬¿ÉµÃ|CD|£®ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬ÓëÍÖÔ²·½³ÌÁªÁ¢»¯Îªx2-mx+m2-3=0£¬ÀûÓÃÏÒ³¤¹«Ê½¿ÉµÃ$|{AB}|=\sqrt{\frac{5}{4}}\sqrt{{{£¨{{x_1}+{x_2}}£©}^2}-4{x_1}{x_2}}$£¬ÀûÓÃ$|{AB}|=\frac{{5\sqrt{3}}}{4}|{CD}|$£¬½âµÃm£®

½â´ð ½â£º£¨1£©ÓÉÌâÒâÖª$\left\{{\begin{array}{l}{b=\sqrt{3}}\\{\frac{c}{a}=\frac{1}{2}}\\{{b^2}={a^2}-{c^2}}\end{array}}\right.⇒\left\{{\begin{array}{l}{a=2}\\{b=\sqrt{3}}\\{c=1}\end{array}}\right.$£¬
¡àÍÖÔ²CµÄ·½³ÌΪ$\frac{x^2}{4}+\frac{y^2}{3}=1$£®
£¨2£©ÓÉ£¨1£©ÖªÔ²x2+y2=1£¬Ô²ÐÄ£¨0£¬0£©µ½lµÄ¾àÀë$d=\frac{2|m|}{{\sqrt{5}}}$£¼1£¬
¡à$|m|£¼\frac{{\sqrt{5}}}{2}$£¬$|{CD}|=2\sqrt{1-\frac{4}{5}{m^2}}$£®
ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬ÁªÁ¢$\left\{{\begin{array}{l}{y=-\frac{1}{2}x+m}\\{\frac{x^2}{4}+\frac{y^2}{3}=1}\end{array}}\right.⇒$x2-mx+m2-3=0£¬
¡÷£¾0⇒${x_1}+{x_2}=m£¬{x_1}{x_2}={m^2}-3$£¬
¡à$|{AB}|=\sqrt{\frac{5}{4}}\sqrt{{{£¨{{x_1}+{x_2}}£©}^2}-4{x_1}{x_2}}$=$\frac{{\sqrt{15}}}{2}\sqrt{4-{m^2}}$£¬
ÓÉ$|{AB}|=\frac{{5\sqrt{3}}}{4}|{CD}|$£¬µÃ${m^2}=\frac{1}{3}$$£¼\frac{5}{4}$£¬¡à$m=¡À\frac{{\sqrt{3}}}{3}$£¬
¹ÊÖ±ÏßlµÄ·½³ÌΪ$l£ºy=-\frac{1}{2}x¡À\frac{{\sqrt{3}}}{3}$£®

µãÆÀ ±¾Ì⿼²éÁËÍÖÔ²µÄ±ê×¼·½³Ì¼°ÆäÐÔÖÊ¡¢Ö±ÏßÓëÍÖÔ²¼°ÆäÔ²ÏཻÏÒ³¤¹«Ê½¡¢µãµ½Ö±ÏߵľàÀ빫ʽ¡¢Ò»Ôª¶þ´Î·½³ÌµÄ¸ùÓëϵÊýµÄ¹Øϵ£¬¿¼²éÁËÍÆÀíÄÜÁ¦Óë¼ÆËãÄÜÁ¦£¬ÊôÓÚÄÑÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

18£®ÒÑÖªº¯Êýf£¨x£©ÊǶ¨ÒåÔÚRÉϵÄżº¯Êý£¬µ±x¡Ý0ʱ£®f£¨x£©=$\left\{\begin{array}{l}{|{x}^{2}-1|£¬0¡Üx¡Ü2}\\{f£¨x-1£©£¬x£¾2}\end{array}\right.$£¬Èôº¯Êýg£¨x£©=f£¨x£©-k£¨x-1£©Ç¡ÓÐ4¸ö²»Í¬µÄÁãµã£¬ÔòʵÊýkµÄÈ¡Öµ·¶Î§ÊÇ£¨¡¡¡¡£©
A£®[-$\frac{3}{4}$£¬-$\frac{3}{5}$£©¡È£¨$\frac{3}{5}$£¬$\frac{3}{4}$]B£®[-1£¬-$\frac{3}{4}$£©¡È£¨$\frac{3}{4}$£¬1]C£®£¨$\frac{3}{5}$£¬$\frac{3}{4}$]D£®[-$\frac{3}{4}$£¬-$\frac{3}{5}$£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

19£®ÒÑÖªF2ΪÍÖÔ²mx2+y2=4m£¨0£¼m£¼1£©µÄÓÒ½¹µã£¬µãA£¨0£¬2£©£¬µãPΪÍÖÔ²ÉÏÈÎÒâÒ»µã£¬ÇÒ|PA|-|PF2|µÄ×îСֵΪ$-\frac{4}{3}$£¬Ôòm=$\frac{2}{9}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

16£®ÔÚ¡÷ABCÖУ¬½ÇA¡¢B¡¢CËù¶ÔµÄ±ß·Ö±ðΪa£¬b£¬c£¬ÇÒsinA£¬sinB£¬sinC³ÉµÈ±ÈÊýÁУ®
£¨¢ñ£©Èôa+c=$\sqrt{3}$£¬B=60¡ã£¬Çóa£¬b£¬cµÄÖµ£»
£¨¢ò£©Çó½ÇBµÄÈ¡Öµ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

3£®ÒÑÖªµÈ²îÊýÁÐ{an}µÄÇ°nÏîºÍΪSn£¬ÇÒS3=6£¬S5=15£®
£¨1£©ÇóÊýÁÐ{an}µÄͨÏʽ£»
£¨2£©Áîbn=2an£¬ÇóÊýÁÐ{bn}µÄÇ°nÏîºÍTn£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

13£®É躯Êýf£¨x£©=3|x|£¬Ôòf£¨x£©ÔÚÇø¼ä£¨m-1£¬2m£©Éϲ»Êǵ¥µ÷º¯Êý£¬ÔòʵÊýmµÄÈ¡Öµ·¶Î§ÊÇ£¨0£¬1£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

20£®Èô${£¨1-\sqrt{2}£©^5}$=a+b$\sqrt{2}$£¨a£¬bΪÓÐÀíÊý£©£¬Ôòa+b=£¨¡¡¡¡£©
A£®32B£®12C£®0D£®-1

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

17£®Èçͼ£¬ÔÚËÄÀâ׶S-ABCDÖУ¬AB¡ÍAD£¬AB¡ÎCD£¬CD=3AB=3£¬Æ½ÃæSAD¡ÍƽÃæABCD£¬EÊÇÏ߶ÎADÉÏÒ»µã£¬AE=ED=$\sqrt{3}$£¬SE¡ÍAD£®
£¨I£©Ö¤Ã÷£ºBE¡ÍSC
£¨II£©£¨ÎÄ£©ÈôSE=1£¬ÇóµãEµ½Æ½ÃæSBCµÄ¾àÀ룮
£¨Àí£©ÈôSE=1£¬Çó¶þÃæ½ÇB-SC-DƽÃæ½ÇµÄÓàÏÒÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

18£®¶¨ÒåÔÚ£¨-1£¬1£©Éϵĺ¯Êýf£¨x£©Âú×㣺µ±x£¬y¡Ê£¨-1£¬1£©Ê±£¬f£¨x£©-f£¨y£©=f£¨$\frac{x-y}{1-xy}$£©£¬²¢ÇÒµ±x¡Ê£¨-1£¬0£©Ê±£¬f£¨x£©£¾0£»ÈôP=f£¨$\frac{1}{3}$£©+f£¨$\frac{1}{4}$£©£¬Q=f£¨$\frac{1}{2}$£©£¬R=f£¨0£©£¬ÔòP¡¢Q¡¢RµÄ´óС¹ØϵΪR£¾Q£¾P£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸