8£®ÔÚÆ½ÃæÖ±½Ç×ø±êϵxOyÖУ¬¶ÔÓÚÖ±Ïßl£ºax+by+c=0ºÍµãP1£¨x1£¬y1£©£¬P2£¨x2£¬y2£©£¬ÈôP1P2¡Íl£¬´¹×ãΪP0£¬ÇÒ$\overrightarrow{{P_1}{P_0}}=¦Ë•\;\overrightarrow{{P_0}{P_2}}$£¬Ôò³ÆµãP1£¬P2¹ØÓÚÖ±Ïßl³É¡°¦Ë¶Ô³Æ¡±£®ÈôÇúÏßCÉÏ´æÔÚµãP1£¬P2¹ØÓÚÖ±Ïßl³É¡°¦Ë¶Ô³Æ¡±£¬Ôò³ÆÇúÏßCΪ¡°¦Ë¶Ô³ÆÇúÏß¡±£®
£¨1£©ÉèP1£¨0£¬3£©£¬P2£¨3£¬0£©£¬ÈôµãP1£¬P2¹ØÓÚÖ±Ïßl³É¡°$\frac{1}{2}$¶Ô³Æ¡±£¬ÇóÖ±ÏßlµÄ·½³Ì£»
£¨2£©ÉèÖ±Ïßl£ºx-y+1=0£¬ÅжÏË«ÇúÏßx2-y2=1ÊÇ·ñΪ¡°¦Ë¶Ô³ÆÇúÏß¡±£¿Çë˵Ã÷ÀíÓÉ£»
£¨3£©ÉèÖ±Ïßl£ºx+y=0£¬ÇÒÅ×ÎïÏßy=x2-mΪ¡°2¶Ô³ÆÇúÏß¡±£¬ÇóʵÊýmµÄȡֵ·¶Î§£®

·ÖÎö £¨1£©ÉèP0£¨x0£¬y0£©£¬ÓÉ$\overrightarrow{{P}_{1}{P}_{0}}$=$\frac{1}{2}$$\overrightarrow{{P}_{0}{P}_{2}}$£¬¿ÉµÃx0=1£¬y0=2£¬¼´¿ÉÇóÖ±ÏßlµÄ·½³Ì£»
£¨2£©Ö±Ïßl£ºx-y+1=0ÓëÆäÖн¥½üÏßx-y=0ƽÐУ¬Ë«ÇúÏßx2-y2=1²»ÊÇΪ¡°¦Ë¶Ô³ÆÇúÏß¡±£»
£¨3£©ÉèÖ±ÏßP1P2£ºy=x+t£¬ÓÉ$\left\{{\begin{array}{l}{y=x+t}\\{y={x^2}-m}\end{array}}\right.$⇒x2-x-t-m=0£¬ÓÉ$\overrightarrow{{P}_{1}{P}_{0}}$=2$\overrightarrow{{P}_{0}{P}_{2}}$£¬¿ÉµÃx0=$\frac{{x}_{1}+2{x}_{2}}{3}$£¬y0=$\frac{{y}_{1}+2{y}_{2}}{3}$£¬´úÈëx0+y0=0µÃx1+2x2+y1+2y2=0£¬»¯¼ò£¬¼´¿ÉÇóʵÊýmµÄȡֵ·¶Î§£®

½â´ð ½â£º£¨1£©ÓÉÌâÒ⣺$\overrightarrow{{P}_{1}{P}_{2}}$=£¨3£¬-3£©¡­£¨1·Ö£©
ÉèP0£¨x0£¬y0£©£¬ÓÉ$\overrightarrow{{P}_{1}{P}_{0}}$=$\frac{1}{2}$$\overrightarrow{{P}_{0}{P}_{2}}$£¬
¿ÉµÃ2£¨x0-0£©=3-x0£¬2£¨y0-3£©=0-y0£¬
ËùÒÔx0=1£¬y0=2£¬¡­£¨3·Ö£©
ËùÒÔÖ±Ïßl£º3£¨x-1£©-3£¨y-2£©=0£¬
¼´ËùÇóÖ±Ïßl£ºx-y+1=0£»                                    ¡­£¨4·Ö£©
£¨2£©Ë«ÇúÏßx2-y2=1²»ÊÇΪ¡°¦Ë¶Ô³ÆÇúÏß¡±¡­£¨6·Ö£©
ÊÂʵÉÏ£¬Ë«ÇúÏßx2-y2=1µÄÁ½Ìõ½¥½üÏß·Ö±ðΪx-y=0£¬x+y=0£¬ËüÃÇ»¥Ïà´¹Ö±£¬
Ö±Ïßl£ºx-y+1=0ÓëÆäÖн¥½üÏßx-y=0ƽÐУ¬
ËùÒÔË«ÇúÏßx2-y2=1Éϲ»¿ÉÄÜ´æÔÚÁ½µãP1£¬P2£¬¸ü±ð˵Âú×ã$\overrightarrow{{P_1}{P_0}}=¦Ë•\;\overrightarrow{{P_0}{P_2}}$  ¡­£¨8·Ö£©
£¨3£©ÒòΪÅ×ÎïÏßy=x2-mΪ¡°2¶Ô³ÆÇúÏß¡±£¬ËùÒÔ´æÔÚµãP1£¨x1£¬y1£©£¬P2£¨x2£¬y2£©£¬
ÉèÖ±ÏßP1P2£ºy=x+t£¬ÓÉ$\left\{{\begin{array}{l}{y=x+t}\\{y={x^2}-m}\end{array}}\right.$⇒x2-x-t-m=0
ÆäÖС÷=1-4£¨-t-m£©£¾0£¬ÇÒ$\left\{{\begin{array}{l}{{x_1}+{x_2}=1}\\{{x_1}{x_2}=-t-m}\end{array}}\right.$
ÓÖÓÉ$\overrightarrow{{P}_{1}{P}_{0}}$=2$\overrightarrow{{P}_{0}{P}_{2}}$£¬¿ÉµÃx0=$\frac{{x}_{1}+2{x}_{2}}{3}$£¬y0=$\frac{{y}_{1}+2{y}_{2}}{3}$
´úÈëx0+y0=0µÃx1+2x2+y1+2y2=0
ËùÒÔx1+xy2+£¨x1+t£©+2£¨x2+t£©=0$⇒{x_2}=-\frac{3}{2}t-1£¬{x_1}=2+\frac{3}{2}t$¡­£¨12·Ö£©
ÓÉ¡÷=1-4£¨-t-m£©=1-4x1x2£¾0µÃ$1-4£¨-\frac{3t}{2}-1£©£¨2+\frac{3t}{2}£©£¾0$⇒t¡Ù-1¡­£¨14·Ö£©
ÓÉx1x2=-t-mµÃm=-t-x1x2=$-t-£¨-\frac{3t}{2}-1£©£¨2+\frac{3t}{2}£©$=$\frac{9}{4}{t^2}+\frac{7}{2}t+2$=$\frac{9}{4}{£¨t+\frac{7}{9}£©^2}+\frac{23}{36}$¡Ê[$\frac{23}{36}$£¬+¡Þ£©£®
¼´ËùÇóʵÊýmµÄ·¶Î§Îª[$\frac{23}{36}$£¬+¡Þ£©£®¡­£¨16·Ö£©

µãÆÀ ±¾ÌâÖ÷Òª¿¼²éж¨Ò壬ֱÏßµÄÒ»°ãʽ·½³Ì£¬ÇóµãµÄ¹ì¼£·½³Ì£¬ÊôÓÚÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

4£®É輯ºÏ$S=\left\{{x¡ÊN\left|{\frac{5}{x}¡Ý1}\right.}\right\}$£¬T={2£¬4£¬6}£¬Ôò¼¯ºÏS¡ÉTÖÐÔªËØ¸öÊýΪ2£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

5£®Èñ½Ç¡÷ABCÖУ¬½ÇA£¬B£¬CËù¶ÔµÄ±ß·Ö±ðΪa£¬b£¬c£¬bcosA+acosB=$\sqrt{3}$R£¬£¨RΪ¡÷ABCÍâ½ÓÔ²µÄ°ë¾¶£©£¬Èôc=2£¬Ôò¡÷ABCÃæ»ýµÄ×î´óֵΪ$\sqrt{3}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

16£®ÒÑÖªº¯Êýf£¨x£©=$\left\{\begin{array}{l}{1+\frac{4}{x}£¬x¡Ý4}\\{lo{g}_{2}x£¬x£¼4}\end{array}\right.$£¬Èô¹ØÓÚxµÄ·½³Ìf£¨x£©=kÓÐÁ½¸ö²»Í¬µÄ¸ù£¬ÔòʵÊýkµÄȡֵ·¶Î§ÊÇ£¨¡¡¡¡£©
A£®£¨-¡Þ£¬1£©B£®£¨-¡Þ£¬2£©C£®[1£¬2£©D£®£¨1£¬2£©

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

3£®ÔÚÆ½ÃæÖ±½Ç×ø±êϵxoyÖУ¬ÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÀëÐÄÂÊΪ$\frac{1}{2}$£¬¹ýÍÖÔ²CµÄÓÒ½¹µãF×÷Á½Ìõ»¥Ïà´¹Ö±µÄÏÒEFÓëMN£¬µ±Ö±ÏßEFбÂÊΪ0ʱ£¬|EF|+|MN|=7£®
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨2£©Çó|EF|+|MN|µÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

13£®ÒÑÖªº¯Êýf£¨x£©=$\frac{1}{3}$x3-$\frac{1}{2}$ax2+£¨b-1£©x+c£¨a£¾0£©£¬ÇúÏßy=f£¨x£©ÔÚµãP£¨0£¬f£¨0£©£©´¦µÄÇÐÏß·½³ÌΪy=x+1
£¨1£©Çób¡¢cµÄÖµ£»
£¨2£©Èô¹ýµã£¨0£¬3£©¿É×÷ÇúÏßg£¨x£©=f£¨x£©-xµÄÈýÌõ²»Í¬ÇÐÏߣ¬ÇóʵÊýaµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

20£®ÒÑÖªÍÖÔ²$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÀëÐÄÂÊΪ$\frac{\sqrt{3}}{2}$£¬ÇÒ¹ýµã£¨$\sqrt{3}$£¬$\frac{1}{2}$£©£®
£¨1£©ÇóÍÖÔ²µÄ±ê×¼·½³Ì£»
£¨2£©ËıßÐÎABCDµÄ¶¥µãÔÚÍÖÔ²ÉÏ£¬ÇÒ¶Ô½ÇÏßAC£¬BD¹ýÔ­µãO£¬ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬Âú×ã4y1y2=x1x2£®
¢ÙÊÔÖ¤kAB+kBCµÄֵΪ¶¨Öµ£¬²¢Çó³ö´Ë¶¨Öµ£»
¢ÚÊÔÇóËıßÐÎABCDÃæ»ýµÄ×î´óÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

17£®ÒÑÖªº¯Êýf£¨x£©=$\frac{x}{2ax+1}$£®
£¨1£©Ö¤Ã÷£ºµ±x¡Ý0ʱ£¬e-2x¡Ý£¨$\frac{x}{x+1}$£©2+2e-x-1£»
£¨2£©É躯Êýg£¨x£©=1-e-x£¬Èôµ±x¡Ý0ʱ£¬g£¨x£©¡Üf£¨x£©ºã³ÉÁ¢£¬ÇóʵÊýaµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

18£®ÒÑÖªa=${log}_{2}\frac{1}{3}$£¬b=lg5£¬c=ln$\sqrt{e}$£¬Ôòa¡¢b¡¢cµÄ´óС¹ØÏµÎª£¨¡¡¡¡£©
A£®£¼b£¼aB£®c£¼a£¼bC£®a£¼c£¼bD£®a£¼b£¼c

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸