·ÖÎö £¨1£©µãбʽÉè³öÖ±ÏßlµÄ·½³Ì²¢ÓëÅ×ÎïÏß·½³ÌÁªÁ¢·½³Ì×飬µÃµ½Ö±ÏßlÓëÎïÏß½»ÓÚA£¬BÁ½µãµÄ×ø±ê¼äµÄ¹Øϵ£¬ÓÉ$\overrightarrow{OP}=\frac{1}{2}\overrightarrow{OA}+\frac{1}{2}\overrightarrow{OB}$£¬µÃµ½µãPµÄ×ø±êÓëÖ±ÏßбÂÊkµÄ¹Øϵ£¬ÏûÈ¥kµÃµ½¶¯µãPµÄ¹ì¼£·½³Ì£®
£¨2£©ÏÈÇó³öÇúÏßCµÄÇÐÏßбÂʦ˵ķ¶Î§£¬ÓÖ$\overrightarrow{MB}=¦Ë\overrightarrow{MA}$£¬Óæ˱íʾa£¬ÓÉбÂʦ˵ķ¶Î§µÃ³öaµÄÈ¡Öµ·¶Î§£®
½â´ð ½â£º£¨1£©ÉèÖ±ÏßlµÄ·½³ÌΪy=k£¨x-1£©£¬½»µãΪA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£®
ÓÉ$\left\{\begin{array}{l}{x^2}=2y\\ y=k£¨x-1£©\end{array}\right.$£¬µÃx2-2kx+2k=0£¬¡£¨1·Ö£©
ÒòΪֱÏßÓëÅ×ÎïÏßÓÐÁ½¸ö½»µã£¬ËùÒÔ¡÷=4k2-8k£¾0£¬¼´k£¾2»òk£¼0..¡£¨2·Ö£©
Ôò$\left\{\begin{array}{l}{x_1}+{x_2}=2k\\{x_1}{x_2}=2k\end{array}\right.$£®¡£¨3·Ö£©
ÓÉ$\overrightarrow{OP}=\frac{1}{2}\overrightarrow{OA}+\frac{1}{2}\overrightarrow{OB}$£¬µÃPÊÇABµÄÖе㣬ÉèP£¨x£¬y£©£¬
Ôò$\left\{\begin{array}{l}x=\frac{{{x_1}+{x_2}}}{2}=k\\ y=k£¨x-1£©={k^2}-k\end{array}\right.$£¬ÏûÈ¥kµÃy=x2-x£¬¡£¨4·Ö£©
ÓÉPµãÔÚyÖáµÄÓҲ࣬µÃx£¾0£¬ÔÙÓÉx=k£¬¼°k£¾2»òk£¼0£¬µÃx£¾2£®¡£¨5·Ö£©
¹Ê¶¯µãPµÄ¹ì¼£·½³ÌΪy=x2-x£¨x£¾2£©£®¡£¨6·Ö£©
£¨2£©ÓÉÇúÏßCµÄ·½³ÌΪy=x2-x£¨x£¾2£©£¬ÇúÏßCµÄÇÐÏßµÄбÂÊΪ¦Ë=y'=2x-1£¨x£¾2£©£¬¡à¦Ë£¾3£®¡£¨7·Ö£©
ÓÉÒÑÖªµÃ£º$\left\{\begin{array}{l}\overrightarrow{MB}=£¨{x_2}-1£¬{y_2}£©\\ \overrightarrow{MA}=£¨{x_1}-1£¬{y_1}£©\end{array}\right.$
ÓÉ$\overrightarrow{MB}=¦Ë\overrightarrow{MA}$µÃ$\left\{\begin{array}{l}{x_2}-1=¦Ë£¨{x_1}-1£©\\{y_2}=¦Ë{y_1}\end{array}\right.$£¬ÓÉ${x_1}^2=2{y_1}$£¬${x_2}^2=2{y_2}$µÃ$\left\{\begin{array}{l}{x_2}=¦Ë{x_1}-¦Ë+1\\{x_2}^2=¦Ë{x_1}^2\end{array}\right.$
Ó֦ˣ¾3½âµÃ$¦Ë{x_1}^2-2¦Ë{x_1}+¦Ë-1=0$£¬¡£¨9·Ö£©
½âµÃ${x_1}=\frac{{2¦Ë¡À\sqrt{4¦Ë}}}{2¦Ë}=1¡À\sqrt{\frac{1}{¦Ë}}$£®
ÔòAµ½yÖáµÄ¾àÀëΪ$a={x_1}=1¡À\sqrt{\frac{1}{¦Ë}}£¨¦Ë£¾3£©$£¬
¹ÊaµÄÈ¡Öµ·¶Î§ÊÇ$£¨1-\frac{{\sqrt{3}}}{3}£¬1£©¡È£¨1£¬1+\frac{{\sqrt{3}}}{3}£©$£®¡£¨12·Ö£©
µãÆÀ ±¾Ì⿼²éÅ×ÎïÏß·½³Ì¡¢¹ì¼£·½³ÌµÄÇ󷨣¬ÒÔ¼°ÏòÁ¿ÔËË㣬¿¼²éѧÉú·ÖÎö½â¾öÎÊÌâµÄÄÜÁ¦£¬ÊôÓÚÖеµÌ⣮
Ä꼶 | ¸ßÖÐ¿Î³Ì | Ä꼶 | ³õÖÐ¿Î³Ì |
¸ßÒ» | ¸ßÒ»Ãâ·Ñ¿Î³ÌÍƼö£¡ | ³õÒ» | ³õÒ»Ãâ·Ñ¿Î³ÌÍƼö£¡ |
¸ß¶þ | ¸ß¶þÃâ·Ñ¿Î³ÌÍƼö£¡ | ³õ¶þ | ³õ¶þÃâ·Ñ¿Î³ÌÍƼö£¡ |
¸ßÈý | ¸ßÈýÃâ·Ñ¿Î³ÌÍƼö£¡ | ³õÈý | ³õÈýÃâ·Ñ¿Î³ÌÍƼö£¡ |
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ
A£® | 3 | B£® | 2 | C£® | -2 | D£® | -3 |
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ
A£® | 5 | B£® | 6 | C£® | 7 | D£® | 8 |
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ
²é¿´´ð°¸ºÍ½âÎö>>
°Ù¶ÈÖÂÐÅ - Á·Ï°²áÁбí - ÊÔÌâÁбí
ºþ±±Ê¡»¥ÁªÍøÎ¥·¨ºÍ²»Á¼ÐÅÏ¢¾Ù±¨Æ½Ì¨ | ÍøÉÏÓк¦ÐÅÏ¢¾Ù±¨×¨Çø | µçÐÅթƾٱ¨×¨Çø | ÉæÀúÊ·ÐéÎÞÖ÷ÒåÓк¦ÐÅÏ¢¾Ù±¨×¨Çø | ÉæÆóÇÖȨ¾Ù±¨×¨Çø
Î¥·¨ºÍ²»Á¼ÐÅÏ¢¾Ù±¨µç»°£º027-86699610 ¾Ù±¨ÓÊÏ䣺58377363@163.com