ÌâÄ¿ÄÚÈÝ
1£®ÒÑÖªµãOÎª×ø±êԵ㣬FΪÍÖÔ²C£º$\frac{x^2}{3}+{y^2}$=1µÄ×󽹵㣬µãP¡¢QÔÚÍÖÔ²ÉÏ£¬µãP¡¢Q¡¢RÂú×ã$\overrightarrow{OF}$•$\overrightarrow{PQ}$=0£¬$\overrightarrow{QR}$+2$\overrightarrow{PQ}$=$\overrightarrow{0}$£¬Ôò$\sqrt{3}|{PF}|+|{OR}$|µÄ×î´óֵΪ£¨¡¡¡¡£©| A£® | 6 | B£® | $\sqrt{3}$£¨1+$\sqrt{2}$+$\sqrt{3}$£© | C£® | 3+3$\sqrt{2}$ | D£® | 3+3$\sqrt{3}$ |
·ÖÎö ÓÉÌâÒ⣬P£¬Q¹ØÓÚxÖá¶Ô³Æ£¬ÉèP£¨x£¬y£©£¬ÔòR£¨x£¬3y£©£¬ÓÃ×ø±ê±íʾ³ö$\sqrt{3}|{PF}|+|{OR}$|£¬ÔÙ»»Ôª£¬¼´¿ÉÇó³ö$\sqrt{3}|{PF}|+|{OR}$|µÄ×î´óÖµ£®
½â´ð ½â£ºÓÉÌâÒ⣬P£¬Q¹ØÓÚxÖá¶Ô³Æ£¬ÉèP£¨x£¬y£©£¬ÔòR£¨x£¬3y£©£¬
¡ßF£¨-$\sqrt{2}$£¬0£©£¬
¡à$\sqrt{3}|{PF}|+|{OR}$|=$\sqrt{3}$•$\sqrt{£¨x+\sqrt{2}£©^{2}+{y}^{2}}$+$\sqrt{{x}^{2}+9{y}^{2}}$=|$\sqrt{2}$x+3|+$\sqrt{9-2{x}^{2}}$£¬
Éè$\sqrt{2}$x=3cos¦Á£¨0£¼¦Á£¼¦Ð£©£¬Ôò$\sqrt{3}|{PF}|+|{OR}$|=|3cos¦Á+3|+3sin¦Á=3+3$\sqrt{2}$sin£¨¦Á+$\frac{¦Ð}{4}$£©
¡àsin£¨¦Á+$\frac{¦Ð}{4}$£©=1ʱ£¬$\sqrt{3}|{PF}|+|{OR}$|µÄ×î´óֵΪ3+3$\sqrt{2}$£¬
¹ÊÑ¡£ºC£®
µãÆÀ ±¾Ì⿼²éÇó$\sqrt{3}|{PF}|+|{OR}$|µÄ×î´óÖµ£¬¿¼²éÈý½Çº¯Êý֪ʶµÄÔËÓã¬ÊôÓÚÖеµÌ⣮
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿
18£®-90¡ã+k•360¡ã£¨k¡Êz£©±íʾµÄÊÇ£¨¡¡¡¡£©
| A£® | µÚÒ»ÏóÏÞ½Ç | B£® | µÚÈýÏóÏÞ½Ç | C£® | ½çÏÞ½Ç | D£® | µÚËÄÏóÏÞ½Ç |
5£®ÒÑÖªº¯Êýf£¨x£©=$\sqrt{3}$sin¦Øxcos¦Øx+sin2¦Øx£¨¦Ø£¾0£©µÄ×îСÕýÖÜÆÚΪ¦Ð£¬½«º¯Êýf£¨x£©µÄͼÏóÏòÓÒÆ½ÒƦգ¨¦Õ£¾0£©¸öµ¥Î»ºó£¬µÃµ½µÄº¯Êý¹ØÓڵ㣨-$\frac{¦Ð}{4}$£¬$\frac{1}{2}$£©¶Ô³Æ£¬Ôò¦ÕµÄÖµ²»¿ÉÄÜΪ£¨¡¡¡¡£©
| A£® | $\frac{¦Ð}{6}$ | B£® | $\frac{2¦Ð}{3}$ | C£® | $\frac{5¦Ð}{3}$ | D£® | $\frac{7¦Ð}{3}$ |
11£®ÈçͼËùʾ£¬Õý·½ÌåABCD-A1B1C1D1ÖУ¬M£¬N·Ö±ðΪÀâC1D1£¬C1CµÄÖе㣬ÒÔÏÂËĸö½áÂÛÖÐÕýÈ·µÄÊÇ£¨¡¡¡¡£©
| A£® | Ö±ÏßMNÓëDC1»¥Ïà´¹Ö± | B£® | Ö±ÏßAMÓëBN»¥ÏàÆ½ÐÐ | ||
| C£® | Ö±ÏßMNÓëBC1Ëù³É½ÇΪ90¡ã | D£® | Ö±ÏßMN´¹Ö±ÓÚÆ½ÃæA1BCD1 |