2£®Èçͼ£¬ÒÑÖªF1¡¢F2·Ö±ðÊÇÍÖÔ²$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄ×ó¡¢ÓÒ½¹µã£¬¶¥µãBµÄ×ø±êÊÇ£¨0£¬b£©£¬Á¬½ÓBF2²¢ÑÓ³¤½»ÍÖÔ²ÓÚµãM£¬µãM¹ØÓÚxÖáµÄ¶Ô³ÆµãΪN£¬Á¬½ÓF1¡¢N£®
£¨I£©ÈôµãNµÄ×ø±êΪ£¨$\frac{8}{3}$£¬$\frac{2}{3}$£©£¬ÇÒBF2=2$\sqrt{2}$£¬ÇóÍÖÔ²µÄ·½³Ì£»
£¨¢ò£©ÈôF1N¡ÍMB£¬ÇóÍÖÔ²ÀëÐÄÂÊeµÄÖµ£®

·ÖÎö £¨¢ñ£©¸ù¾ÝÍÖÔ²µÄ¶¨Ò壬½¨Á¢·½³Ì¹Øϵ¼´¿ÉÇó³öa£¬bµÄÖµ£¬¼´¿ÉµÃµ½ÍÖÔ²·½³Ì£»
£¨¢ò£©Çó³öCµÄ×ø±ê£¬ÀûÓÃF1C¡ÍAB½¨Á¢Ð±ÂÊÖ®¼äµÄ¹Øϵ£¬½â·½³Ì¼´¿ÉÇó³öeµÄÖµ£®

½â´ð ½â£º£¨I£©¡ßNµÄ×ø±êΪ£¨$\frac{8}{3}$£¬$\frac{2}{3}$£©£¬
¡à$\frac{\frac{64}{9}}{{a}^{2}}$+$\frac{\frac{4}{9}}{{b}^{2}}$=1£¬¼´$\frac{64}{{a}^{2}}$+$\frac{4}{{b}^{2}}$=9£¬
¡ßBF22=b2+c2=a2£¬
¡àa2=£¨2$\sqrt{2}$£©2=8£¬¼´b2=4£¬
ÔòÍÖÔ²µÄ·½³ÌΪ$\frac{{x}^{2}}{8}$+$\frac{{y}^{2}}{4}$=1£»
£¨¢ò£©ÉèF1£¨-c£¬0£©£¬F2£¨c£¬0£©£¬
¡ßB£¨0£¬b£©£¬
¡àÖ±ÏßBF2£ºy=-$\frac{b}{c}$x+b£¬
´úÈëÍÖÔ²·½³Ì$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÃ£¨$\frac{1}{{a}^{2}}$+$\frac{1}{{c}^{2}}$£©x2-$\frac{2}{c}$x=0£¬
½âµÃx=0£¬»òx=$\frac{2{a}^{2}c}{{a}^{2}+{c}^{2}}$£¬
¡ßM£¨$\frac{2{a}^{2}c}{{a}^{2}+{c}^{2}}$£¬$\frac{b£¨{c}^{2}-{a}^{2}£©}{{a}^{2}+{c}^{2}}$£©£¬ÇÒM£¬N¹ØÓÚxÖá¶Ô³Æ£¬
¡àN£¨$\frac{2{a}^{2}c}{{a}^{2}+{c}^{2}}$£¬-$\frac{b£¨{c}^{2}-{a}^{2}£©}{{a}^{2}+{c}^{2}}$£©£¬
Ôò${k}_{{F}_{1}N}$=-$\frac{\frac{b£¨{c}^{2}-{a}^{2}£©}{{a}^{2}+{c}^{2}}}{\frac{2{a}^{2}c}{{a}^{2}+{c}^{2}}+c}$=$\frac{{a}^{2}b-b{c}^{2}}{3{a}^{2}c+{c}^{3}}$£¬
¡ßF1N¡ÍMB£¬
¡à$\frac{{a}^{2}b-b{c}^{2}}{3{a}^{2}c+{c}^{3}}$•£¨-$\frac{b}{c}$£©=-1£¬
ÓÉb2=a2-c2µÃ$\frac{{c}^{2}}{{a}^{2}}$=$\frac{1}{5}$£¬
¼´e=$\frac{c}{a}$=$\frac{\sqrt{5}}{5}$£®

µãÆÀ ±¾ÌâÖ÷Òª¿¼²éԲ׶ÇúÏßµÄ×ÛºÏÎÊÌ⣬ҪÇóÊìÁ·ÕÆÎÕÍÖÔ²·½³ÌµÄÇó·¨ÒÔ¼°Ö±Ïß´¹Ö±ºÍбÂÊÖ®¼äµÄ¹Øϵ£¬ÔËËãÁ¿½Ï´ó£®

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

12£®ÒÑÖªÔ²x2+y2+4x-8y-16=0£¬ÔòÔ²ÐĵÄ×ø±êΪ£¨-2£¬4£©£¬°ë¾¶Îª6£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

13£®¿Õ¼ä²»¹²ÏßµÄËĵ㣬¿ÉÒÔÈ·¶¨Æ½ÃæµÄ¸öÊýÊÇ£¨¡¡¡¡£©
A£®0B£®1C£®1»ò4D£®ÎÞ·¨È·¶¨

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

10£®ÒÑÖªÖ±ÏßlµÄбÂÊk=2£¬²¢ÇÒ¾­¹ýÒ»µã£¨2£¬-3£©ÔòÖ±Ïߵĵãбʽ·½³ÌΪ£¨¡¡¡¡£©
A£®y-3=2£¨x-2£©B£®y+3=2£¨x-2£©C£®y-2=k£¨x+3£©D£®y-2=2£¨x-3£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

17£®Æ溯Êýf£¨x£©ÊǶ¨ÒåÓòΪRµÄÖÜÆÚº¯Êý£¬ÆäÖÜÆÚΪ4£¬µ±x¡Ê£¨-2£¬0£©Ê±f£¨x£©=2x£¬f£¨2012£©-f£¨2011£©=-$\frac{1}{2}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

7£®Èôij¼¸ºÎÌåµÄÈýÊÓͼÈçͼËùʾ£¬ÆäÖÐA1M£ºAM=7£º5£®Ôò´Ë¼¸ºÎÌåµÄÌå»ýµÈÓÚ£¨¡¡¡¡£©
A£®55B£®62C£®65D£®72

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

14£®ÉèÁ½ÏòÁ¿e1¡¢e2Âú×ã|${\overrightarrow{e}}_{1}$|=2£¬|${\overrightarrow{e}}_{2}$|=1£¬${\overrightarrow{e}}_{1}$¡¢${\overrightarrow{e}}_{2}$µÄ¼Ð½ÇΪ60¡ã£¬ÈôÏòÁ¿2t${\overrightarrow{e}}_{1}$+7${\overrightarrow{e}}_{2}$ÓëÏòÁ¿${\overrightarrow{e}}_{1}$+t${\overrightarrow{e}}_{2}$µÄ¼Ð½ÇΪ[0£¬$\frac{¦Ð}{2}$£©£¬ÇóʵÊýtµÄÈ¡Öµ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

11£®Èôtan¦Á=2£¬Ôò1+sin¦Ácos¦Á=$\frac{7}{5}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

12£®Èôsin¦È•cos¦È£¼0£¬|cos¦È|=cos¦È£¬ÔòµãP£¨tan¦È£¬cos¦È£©ÔÚ£¨¡¡¡¡£©
A£®µÚÒ»ÏóÏÞB£®µÚ¶þÏóÏÞC£®µÚÈýÏóÏÞD£®µÚËÄÏóÏÞ

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸