10£®Èçͼ£¬ÒÑÖªÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÀëÐÄÂÊΪ$\frac{\sqrt{3}}{2}$£¬ÒÔÍÖÔ²CµÄ×ó¶¥µãTΪԲÐÄ×÷Ô²T£º£¨x+2£©2+y2=r2£¨r£¾0£©£¬ÉèÔ²TÓëÍÖÔ²C½»ÓÚµãMÓëµãN£®
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨2£©ÉèµãPÊÇÍÖÔ²CÉÏÒìÓÚM£¬NµÄÈÎÒâÒ»µã£¬ÇÒÖ±ÏßMP£¬NP·Ö±ðÓëxÖá½»ÓÚµãR£¬S£¬OÎª×ø±êÔ­µã£¬Çó|OR|+|OS|µÄ×îСֵ£®

·ÖÎö £¨1£©ÓÉÌâÒâ¿ÉµÃa=2£¬ÔËÓÃÀëÐÄÂʹ«Ê½ºÍa£¬b£¬cµÄ¹ØÏµ£¬¿ÉµÃb£¬½ø¶øµÃµ½ÍÖÔ²·½³Ì£»
£¨2£©ÉèM£¨x1£¬y1£©£¬N£¨x2£¬y2£©£¬P£¨x0£¬y0£©£¬ÇóµÃÖ±ÏßMP£¬NPµÄ·½³Ì£¬Áîy=0£¬ÇóµÃµãR£¬SµÄºá×ø±ê£¬½áºÏM£¬PÂú×ãÍÖÔ²·½³Ì£¬ÇóµÃR£¬SµÄºá×ø±êÖ®»ý£¬ÔÙÓÉ»ù±¾²»µÈʽ¼´¿ÉµÃµ½×îСֵ£®

½â´ð ½â£º£¨1£©ÒÀÌâÒ⣬µÃa=2£¬e=$\frac{c}{a}$=$\frac{\sqrt{3}}{2}$£¬
¡àc=$\sqrt{3}$£¬b=$\sqrt{{a}^{2}-{c}^{2}}$=1£»
¹ÊÍÖÔ²CµÄ·½³ÌΪ$\frac{{x}^{2}}{4}$+y2=1£®
£¨2£©µãMÓëµãN¹ØÓÚxÖá¶Ô³Æ£¬ÉèM£¨x1£¬y1£©£¬N£¨x2£¬y2£©£¬P£¨x0£¬y0£©
ÔòÖ±ÏßMPµÄ·½³ÌΪ£ºy-y0=$\frac{{y}_{0}-{y}_{1}}{{x}_{0}-{x}_{1}}$£¨x-x0£©£¬
Áîy=0£¬µÃxR=$\frac{{x}_{1}{y}_{0}-{x}_{0}{y}_{1}}{{y}_{0}-{y}_{1}}$£¬Í¬Àí£ºxS=$\frac{{x}_{1}{y}_{0}+{x}_{0}{y}_{1}}{{y}_{0}+{y}_{1}}$£¬
¹ÊxRxS=$\frac{{{x}_{1}}^{2}{{y}_{0}}^{2}-{{x}_{0}}^{2}{{y}_{1}}^{2}}{{{y}_{0}}^{2}-{{y}_{1}}^{2}}$ £¨**£© 
ÓÖµãMÓëµãPÔÚÍÖÔ²ÉÏ£¬¹Êx02=4£¨1-y02£©£¬x12=4£¨1-y12£©£¬
´úÈ루**£©Ê½£¬µÃ£º
xRxS=$\frac{4£¨1-{{y}_{1}}^{2}£©{{y}_{0}}^{2}-4£¨1-{{y}_{0}}^{2}£©{{y}_{1}}^{2}}{{{y}_{0}}^{2}-{{y}_{1}}^{2}}$=$\frac{4£¨{{y}_{0}}^{2}-{{y}_{1}}^{2}£©}{{{y}_{0}}^{2}-{{y}_{1}}^{2}}$=4
ËùÒÔ|OR|•|OS|=|xR|•|xS|=|xR•xS|=4£¬
|OR|+|OS|¡Ý2$\sqrt{|OR|•|OS|}$=4£¬
µ±ÇÒ½öµ±|OR|=|OS|=2£¬È¡µÃµÈºÅ£®
Ôò|OR|+|OS|µÄ×îСֵΪ4£®

µãÆÀ ±¾Ì⿼²éÍÖÔ²µÄ·½³ÌºÍÐÔÖÊ£¬Ö÷Òª¿¼²éÀëÐÄÂʺͷ½³ÌµÄÔËÓã¬×¢ÒâµãÂú×ãÍÖÔ²·½³Ì£¬Í¬Ê±¿¼²é»ù±¾²»µÈʽµÄÔËÓ㬾ßÓÐÒ»¶¨µÄÔËËãÁ¿£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

20£®Ö´ÐÐÈçͼËùʾµÄ³ÌÐò¿òͼ£¬Êä³öSµÄֵΪ£¨¡¡¡¡£©
A£®0B£®-1C£®-$\frac{1}{2}$D£®-$\frac{3}{2}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

1£®ì³²¨ÄÇÆõÊýÁÐÊÇ£ºµÚ1ÏîÊÇ0£¬µÚ2ÏîÊÇ1£¬´ÓµÚÈýÏʼ£¬Ã¿Ò»Ïî¶¼µÈÓÚǰÁ½ÏîÖ®ºÍ£®Ä³Í¬Ñ§Éè¼ÆÁËÒ»¸öÇóÕâ¸öÊýÁеÄǰ10ÏîºÍµÄ³ÌÐò¿òͼ£¬ÄÇôÔÚ¿Õ°×¾ØÐοòºÍÅжϿòÄÚÓ¦·Ö±ðÌîÈëµÄÓï¾äÊÇ£¨¡¡¡¡£©
A£®c=a£¬i¡Ü9B£®b=c£¬i¡Ü9C£®c=a£¬i¡Ü10D£®b=c£¬i¡Ü10

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

18£®Èçͼ£¬ÔÚÁâÐÎABCDÖУ¬AB=2£¬¡ÏBAD=60¡ã£¬ÑضԽÇÏßBD½«¡÷ABDÕÛÆð£¬Ê¹A£¬CÖ®¼äµÄ¾àÀëΪ$\sqrt{6}$£¬ÈôP£¬Q·Ö±ðΪÏß¶ÎBD£¬CAÉϵ͝µã£®

£¨1£©ÇóÏß¶ÎPQ³¤¶ÈµÄ×îСֵ£»
£¨2£©µ±Ïß¶ÎPQ³¤¶È×îСʱ£¬ÇóÖ±ÏßPQÓëÆ½ÃæACDËù³É½ÇµÄÕýÏÒÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

5£®ÒÑÖªÈçͼÊÇÒ»¸ö¿Õ¼ä¼¸ºÎÌåµÄÈýÊÓͼ£¬Ôò¸Ã¼¸ºÎÌåµÄÌå»ýΪ£¨¡¡¡¡£©
 
A£®12+$\frac{4¦Ð}{3}$B£®12+$\frac{16¦Ð}{3}$C£®4+$\frac{16¦Ð}{3}$D£®4+$\frac{4¦Ð}{3}$

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

15£®ÔÚÖ±½Ç×ø±êϵxOyÖУ¬ÒÔÔ­µãOΪ¼«µã£¬xÖáµÄÕý°ëÖáΪ¼«Öᣬ½¨Á¢¼«×ø±êϵ£®ÒÑÖªÇúÏßC1£º$\left\{\begin{array}{l}{x=-4+cost}\\{y=3+sint}\end{array}\right.$ £¨tΪ²ÎÊý£©£¬C2£º$\left\{\begin{array}{l}{x=8cos¦È}\\{y=3sin¦È}\end{array}\right.$£¨¦ÈΪ²ÎÊý£©£®
£¨¢ñ£©»¯C1£¬C2µÄ·½³ÌΪÆÕͨ·½³Ì£¬²¢ËµÃ÷ËüÃÇ·Ö±ð±íʾʲôÇúÏߣ»
£¨¢ò£©ÈôC1ÉϵĵãP¶ÔÓ¦µÄ²ÎÊýΪt=$\frac{¦Ð}{2}$£¬QΪC2Éϵ͝µã£¬ÇóPQÖеãMµ½Ö±ÏßC3£º¦Ñ£¨cos¦È-2sin¦È£©=7¾àÀëµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

2£®´óѧÉúСÕԼƻ®ÀûÓÃ¼ÙÆÚ½øÐÐÒ»´Î¶ÌÆÚ´ò¹¤ÌåÑ飬ÒÑ֪СÕÔÏëȥij¹¤³§´ò¹¤£¬ÀÏ°å¸æÖªÃ¿ÌìÉϰàµÄʱ¼ä£¨µ¥Î»£ºÐ¡Ê±£©ºÍ¹¤×Ê£¨µ¥Î»£ºÔª£©£¬Èç±íËùʾ£º
ʱ¼äx2358912
¹¤×Êy30406090120m
¸ù¾Ý¼ÆË㣬СÕÔµÃÖªÕâ¶Îʱ¼äÿÌì´ò¹¤¹¤×ÊÓëÿÌ칤×÷ʱ¼äÂú×ãµÄÏßÐԻع鷽³ÌΪ$\stackrel{¡Ä}{y}$=11.4x+5.9£¬ÈôСÕÔÔÚ¼ÙÆÚÄÚ´ò5Ì칤£¬¹¤×÷ʱ¼ä£¨µ¥Î»£ºÐ¡Ê±£©·Ö±ðΪ8£¬8£¬9£¬9£¬12£¬ÔòÕâ5ÌìСÕÔ»ñµÃ¹¤×ʵķ½²îΪ£¨¡¡¡¡£©
A£®112B£®240C£®376D£®484

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

19£®ÒÑÖªµÈ±ÈÊýÁÐ{an}µÄǰ4ÏîºÍS4=5£¬ÇÒ4a1$£¬\;\frac{3}{2}{a_2}\;£¬\;{a_2}$³ÉµÈ²îÊýÁУ®
£¨¢ñ£©Çó{an}µÄͨÏʽ£»
£¨¢ò£©Éè{bn}ÊÇÊ×ÏîΪ2£¬¹«²îΪ-a1µÄµÈ²îÊýÁУ¬ÆäǰnÏîºÍΪTn£¬ÇóÂú×ãTn-1£¾0µÄ×î´óÕýÕûÊýn£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

20£®ÈçͼÊÇij¼¸ºÎÌåµÄÈýÊÓͼ£¬ÇÒÕýÊÓͼÓë²àÊÓͼÏàͬ£¬ÔòÕâ¸ö¼¸ºÎÌåµÄ±íÃæ»ýÊÇ£¨¡¡¡¡£©
A£®$\frac{4}{3}$¦ÐB£®7¦ÐC£®£¨5+$\sqrt{5}$£©¦ÐD£®£¨4+$\sqrt{5}$£©¦Ð

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸