·ÖÎö £¨1£©ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬Çó³öµ±ÁâÐÎABCDµÄ¶Ô½ÇÏßÔÚ×ø±êÖáÉÏʱµÄÃæ»ý£»µ±ÁâÐÎABCDµÄ¶Ô½ÇÏß²»ÔÚ×ø±êÖáÉÏʱ£¬ÉèÖ±ÏßACµÄ·½³ÌΪ£ºy=kx£¬ÔòÖ±ÏßBDµÄ·½³ÌΪ£º$y=-\frac{1}{k}x$£¬ÁªÁ¢Ö±Ïß·½³ÌºÍÍÖÔ²·½³Ì£¬ÇóµÃOA¡¢OB£¬´úÈëÁâÐÎÃæ»ý¹«Ê½£¬×ª»¯Îª¹ØÓÚkµÄº¯Êý£¬ÔÙÓÉ»ù±¾²»µÈʽÇó×îÖµ£»
£¨2£©ÉèԵ㵽ÁâÐÎÈÎÒ»±ßµÄ¾àÀëΪd£¬½áºÏ£¨1£©ÀûÓõȻý·¨ÇóµÃdΪ¶¨Öµ£¬ËµÃ÷´æÔÚ¶¨Ô²ÓëFÖеÄÁâÐζ¼ÏàÇУ¬²¢ÇóµÃÔ²µÄ·½³Ì£»
£¨3£©ÉèÁâÐεÄÒ»±ßADµÄ·½³ÌΪ$y=t£¨{x-\sqrt{3}}£©$£¬»¯ÎªÒ»°ãʽ£¬ÓÉ£¨2£©½áºÏµãµ½Ö±ÏߵľàÀ빫ʽÇóµÃtµÃ´ð°¸£®
½â´ð ½â£º£¨1£©Èçͼ£¬ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬
¢Ùµ±ÁâÐÎABCDµÄ¶Ô½ÇÏßÔÚ×ø±êÖáÉÏʱ£¬ÆäÃæ»ýΪ$4¡Á\frac{1}{2}¡Á2¡Á1=4$£»
¢Úµ±ÁâÐÎABCDµÄ¶Ô½ÇÏß²»ÔÚ×ø±êÖáÉÏʱ£¬ÉèÖ±ÏßACµÄ·½³ÌΪ£ºy=kx£¬
ÔòÖ±ÏßBDµÄ·½³ÌΪ£º$y=-\frac{1}{k}x$£¬
ÁªÁ¢$\left\{\begin{array}{l}{y=kx}\\{\frac{{x}^{2}}{4}+{y}^{2}=1}\end{array}\right.$£¬µÃ${x_1}^2=\frac{4}{{4{k^2}+1}}$£¬${y_1}^2=\frac{{4{k^2}}}{{4{k^2}+1}}$£¬
´Ó¶ø$O{A^2}={x_1}^2+{y_1}^2=\frac{{4£¨{k^2}+1£©}}{{4{k^2}+1}}$£¬
ͬÀí¿ÉµÃ£¬$O{B^2}={x_2}^2+{y_2}^2=\frac{{4[{{{£¨{-\frac{1}{k}}£©}^2}+1}]}}{{4{{£¨{-\frac{1}{k}}£©}^2}+1}}=\frac{{4£¨{k^2}+1£©}}{{{k^2}+4}}$£¬
¡àÁâÐÎABCDµÄÃæ»ýΪ2¡ÁOA¡ÁOB=$8\sqrt{\frac{{{k^4}+2{k^2}+1}}{{4{k^4}+17{k^2}+4}}}$=$4\sqrt{\frac{{{k^4}+2{k^2}+1}}{{{k^4}+\frac{17}{4}{k^2}+1}}}$
=$4\sqrt{1-\frac{{\frac{9}{4}{k^2}}}{{{k^4}+\frac{17}{4}{k^2}+1}}}$=$4\sqrt{1-\frac{9}{{4£¨{{k^2}+\frac{1}{k^2}}£©+17}}}$$¡Ý4\sqrt{1-\frac{9}{{4¡Á2\sqrt{{k^2}¡Á\frac{1}{k^2}}+17}}}$=$\frac{16}{5}$£®
£¨µ±ÇÒ½öµ±k=¡À1ʱµÈºÅ³ÉÁ¢£©£¬
×ÛÉϵã¬ÁâÐÎABCDµÄ×îÐ¡Ãæ»ýΪ$\frac{16}{5}$£»
£¨2£©´æÔÚ¶¨Ô²${x^2}+{y^2}=\frac{4}{5}$ÓëFÖÐÁâÐεͼÏàÇУ®
ÉèԵ㵽ÁâÐÎÈÎÒ»±ßµÄ¾àÀëΪd£¬ÏÂÃæÖ¤Ã÷£º$d=\frac{2}{{\sqrt{5}}}$£®
Ö¤Ã÷£ºÓÉ£¨1£©Öª£¬µ±ÁâÐÎABCDµÄ¶Ô½ÇÏßÔÚ×ø±êÖáÉÏʱ£¬$d=\frac{2}{{\sqrt{5}}}$£¬
µ±ÁâÐÎABCDµÄ¶Ô½ÇÏß²»ÔÚ×ø±êÖáÉÏʱ£¬
${d^2}=\frac{{O{A^2}¡ÁO{B^2}}}{{O{A^2}+O{B^2}}}$=$\frac{{\frac{{4£¨{k^2}+1£©}}{{4{k^2}+1}}¡Á\frac{{4£¨{k^2}+1£©}}{{{k^2}+4}}}}{{\frac{{4£¨{k^2}+1£©}}{{4{k^2}+1}}+\frac{{4£¨{k^2}+1£©}}{{{k^2}+4}}}}$=$\frac{{4{{£¨{k^2}+1£©}^2}}}{{£¨{k^2}+1£©£¨{k^2}+4£©+£¨{k^2}+1£©£¨4{k^2}+1£©}}$
=$\frac{{4{{£¨{k^2}+1£©}^2}}}{{£¨{k^2}+1£©£¨5{k^2}+5£©}}=\frac{4}{5}$£¬¼´µÃ$d=\frac{2}{{\sqrt{5}}}$£®
×ÛÉÏ£¬´æÔÚ¶¨Ô²${x^2}+{y^2}=\frac{4}{5}$ÓëFÖеÄÁâÐζ¼ÏàÇУ»
£¨3£©ÉèÖ±ÏßADµÄ·½³ÌΪ$y=t£¨{x-\sqrt{3}}£©$£¬¼´$tx-y-\sqrt{3}t=0$£¬
ÔòµãO£¨0£¬0£©µ½Ö±ÏßADµÄ¾àÀëΪ$\frac{{|{\sqrt{3}t}|}}{{\sqrt{{t^2}+1}}}=\frac{2}{{\sqrt{5}}}$£¬
½âµÃ$t=¡À\frac{{2\sqrt{11}}}{11}$£¬
Ö±ÏßADµÄ·½³ÌΪ$y=¡À\frac{{2\sqrt{11}}}{11}£¨{x-\sqrt{3}}£©$£®
µãÆÀ ±¾Ì⿼²éÁËÍÖÔ²µÄ±ê×¼·½³Ì¼°ÆäÐÔÖÊ¡¢Ö±ÏßÓëÍÖÔ²ÏཻÎÊÌâ¡¢»ù±¾²»µÈʽµÄÐÔÖÊ£¬¿¼²éÁËÍÆÀíÄÜÁ¦Óë¼ÆËãÄÜÁ¦£¬ÑµÁ·ÁË´æÔÚÏëÎÊÌâµÄÇó½â·½·¨£¬ÊôÓÚÄÑÌ⣮
| Äê¼¶ | ¸ßÖÐ¿Î³Ì | Äê¼¶ | ³õÖÐ¿Î³Ì |
| ¸ßÒ» | ¸ßÒ»Ãâ·Ñ¿Î³ÌÍÆ¼ö£¡ | ³õÒ» | ³õÒ»Ãâ·Ñ¿Î³ÌÍÆ¼ö£¡ |
| ¸ß¶þ | ¸ß¶þÃâ·Ñ¿Î³ÌÍÆ¼ö£¡ | ³õ¶þ | ³õ¶þÃâ·Ñ¿Î³ÌÍÆ¼ö£¡ |
| ¸ßÈý | ¸ßÈýÃâ·Ñ¿Î³ÌÍÆ¼ö£¡ | ³õÈý | ³õÈýÃâ·Ñ¿Î³ÌÍÆ¼ö£¡ |
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ
| A£® | £¨-$\frac{¦Ð}{4}$£¬0£© | B£® | £¨0£¬0£© | C£® | £¨$\frac{¦Ð}{4}$£¬0£© | D£® | £¨$\frac{¦Ð}{6}$£¬0£© |
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ
| A£® | ÏàÀë | B£® | ÏàÇÐ | C£® | Ïཻ | D£® | ËæmµÄ±ä»¯¶ø±ä»¯ |
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ
| A£® | µÈÑüÖ±½ÇÈý½ÇÐÎ | B£® | Ö±½ÇÈý½ÇÐÎ | ||
| C£® | µÈÑüÈý½ÇÐÎ | D£® | µÈÑü»òÖ±½ÇÈý½ÇÐÎ |
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ
| A£® | £¨0£¬¦Ð£© | B£® | £¨0£¬¦Ð] | C£® | £¨0£¬4¦Ð£© | D£® | £¨0£¬4¦Ð] |
²é¿´´ð°¸ºÍ½âÎö>>
¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ
²é¿´´ð°¸ºÍ½âÎö>>
¹ú¼ÊѧУÓÅÑ¡ - 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