10£®ÒÑÖªÍÖÔ²E£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©£¬ÍÖÔ²EµÄÓÒ½¹µãµ½Ö±Ïßl£ºx-y+1=0µÄ¾àÀëΪ$\sqrt{2}$£®ÍÖÔ²EµÄÓÒ¶¥µãµ½ÓÒ½¹µãÓëÖ±Ïßx=2µÄ¾àÀëÖ®±ÈΪ$\frac{\sqrt{2}}{2}$£®
£¨1£©ÇóÍÖÔ²EµÄ±ê×¼·½³Ì£»
£¨2£©ÈôÖ±ÏßlÓëÍÖÔ²E½»ÓÚM£¬NÁ½µã£¬lÓëxÖᣬyÖá·Ö±ð½»ÓÚC£¬DÁ½µã£¬¼ÇMNµÄÖеãΪG£¬ÇÒC£¬DÁ½µãµ½Ö±ÏßOGµÄ¾àÀëÏàµÈ£¬µ±¡÷OMNµÄÃæ»ý×î´óʱ£¬Çó¡÷OCDµÄÃæ»ý£®

·ÖÎö £¨1£©ÓÉÌâÒâµÃµ½¹ØÓÚa£¬cµÄ·½³Ì£¬Çó³öa£¬cµÄÖµ£¬½áºÏÒþº¬Ìõ¼þÇóµÃb£¬ÔòÍÖÔ²·½³Ì¿ÉÇó£»
£¨2£©Éè³öÖ±ÏßlµÄ·½³Ìy=kx+t£¬ºÍÍÖÔ²·½³ÌÁªÁ¢£¬»¯Îª¹ØÓÚxµÄÒ»Ôª¶þ´Î·½³Ì£¬ÀûÓøùÓëϵÊýµÄ¹ØϵµÃµ½M£¬NµÄºá×ø±êµÄºÍÓë»ý£¬ÔÙÓɵ㵽ֱÏߵľàÀ빫ʽÇó³öOµ½Ö±ÏߵľàÀ룬´úÈëÈý½ÇÐÎÃæ»ý¹«Ê½£¬½áºÏMNµÄÖеãΪG£¬ÇÒC£¬DÁ½µãµ½Ö±ÏßOGµÄ¾àÀëÏàµÈ¿ÉµÃkµÄÖµ£¬°ÑÈý½ÇÐÎÃæ»ýת»¯Îªº¬ÓÐtµÄ¹Øϵʽ£¬ÔòÇó³öʹÈý½ÇÐÎOMNµÄÃæ»ý×î´óʱµÄkÓëtµÄÖµ£¬½øÒ»²½ÇóµÃ¡÷OCDµÄÃæ»ý£®

½â´ð ½â£º£¨1£©ÓÉÌâÒ⣬µÃ$\left\{\begin{array}{l}{\frac{|c+1|}{\sqrt{2}}=\sqrt{2}}\\{\frac{a-c}{|a-2|}=\frac{\sqrt{2}}{2}}\end{array}\right.$£¬½âµÃ$a=\sqrt{2}£¬c=1$£¬
¡àb2=a2-c2=2-1=1£¬
ÔòÍÖÔ²EµÄ±ê×¼·½³ÌΪ$\frac{{x}^{2}}{2}+{y}^{2}=1$£»
£¨2£©Èçͼ£¬ÉèÖ±ÏßlµÄ·½³ÌΪy=kx+t£¬
ÁªÁ¢$\left\{\begin{array}{l}{y=kx+t}\\{\frac{{x}^{2}}{2}+{y}^{2}=1}\end{array}\right.$£¬µÃ£¨1+2k2£©x2+4ktx+2t2-2=0£¬
¡÷=16k2t2-4£¨1+2k2£©£¨2t2-2£©=16k2-8t2+8£¾0£¬
ÉèM£¨x1£¬y1£©£¬N£¨x2£¬y2£©£¬
Ôò${x}_{1}+{x}_{2}=-\frac{4kt}{1+2{k}^{2}}£¬{x}_{1}{x}_{2}=\frac{2{t}^{2}-2}{1+2{k}^{2}}$£¬
ÓÉC£¬DÁ½µãµ½Ö±ÏßOGµÄ¾àÀëÏàµÈ£¬¿ÉÖªGΪCDµÄÖе㣬
ÓÉÖ±Ïß·½³ÌΪy=kx+t£¬
µÃC£¨-$\frac{t}{k}£¬0$£©£¬D£¨0£¬t£©£¬
¡àG£¨$-\frac{t}{2k}£¬\frac{t}{2}$£©£¬
ÓÖGΪMNµÄÖе㣬
¡à$-\frac{t}{2k}=\frac{{x}_{1}+{x}_{2}}{2}=-\frac{2kt}{1+2{k}^{2}}$£¬½âµÃ${k}^{2}=\frac{1}{2}$£¬
´úÈë¡÷=16k2-8t2+8£¾0£¬¿ÉµÃt2£¼2£®
¡à|MN|=$\sqrt{1+{k}^{2}}\sqrt{£¨{x}_{1}+{x}_{2}£©^{2}-4{x}_{1}{x}_{2}}$=$\sqrt{1+{k}^{2}}\sqrt{£¨-\frac{4kt}{1+2{k}^{2}}£©^{2}-4\frac{2{t}^{2}-2}{1+2{k}^{2}}}$
=2$\sqrt{1+{k}^{2}}•\frac{\sqrt{4{k}^{2}-2{t}^{2}+2}}{1+2{k}^{2}}$£®
Ô­µãOµ½Ö±Ïßy=kx+tµÄ¾àÀëd=$\frac{|t|}{\sqrt{{k}^{2}+1}}$£®
¡à${S}_{¡÷OMN}=\frac{1}{2}•\frac{|t|}{\sqrt{{k}^{2}+1}}•2\sqrt{1+{k}^{2}}•\frac{\sqrt{4{k}^{2}-2{t}^{2}+2}}{1+2{k}^{2}}$=$\frac{|t|\sqrt{4{k}^{2}-2{t}^{2}+2}}{1+2{k}^{2}}$£®
´úÈë${k}^{2}=\frac{1}{2}$£¬¿ÉµÃ
${S}_{¡÷OMN}=\frac{\sqrt{2}|t|\sqrt{2-{t}^{2}}}{2}=\frac{\sqrt{2}\sqrt{-{t}^{4}+2{t}^{2}}}{2}$=$\frac{\sqrt{2}}{2}\sqrt{£¨-{t}^{2}-1£©^{2}+1}$£®
ÓÉt2£¼2Öª£¬µ±t2=1ʱ£¬S¡÷OMNÈ¡µÃ×î´óÖµ£¬µÈÓÚ$\frac{\sqrt{2}}{2}$£®
´Ëʱ${t}^{2}=1£¬{k}^{2}=\frac{1}{2}$£¬$|k|=\frac{\sqrt{2}}{2}$£¬
${S}_{¡÷OCD}=\frac{1}{2}|OC|•|OD|=\frac{1}{2}$$|\frac{t}{k}|•|t|$=$\frac{1}{2}•\frac{1}{\frac{\sqrt{2}}{2}}=\frac{\sqrt{2}}{2}$£®

µãÆÀ ±¾Ì⿼²éÍÖÔ²µÄ¼òµ¥ÐÔÖÊ£¬¿¼²éÁËÍÖÔ²·½³ÌµÄÇ󷨣¬Éæ¼°Ö±ÏßÓëԲ׶ÇúÏߵĹØϵÎÊÌ⣬³£ÁªÁ¢Ö±Ïß·½³ÌºÍԲ׶ÇúÏß·½³Ì£¬»¯Îª¹ØÓÚxµÄÒ»Ôª¶þ´Î·½³Ìºó£¬ÀûÓøùÓëϵÊýµÄ¹ØϵÇó½â£¬ÊÇѹÖáÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

20£®ÒÑÖªÃݺ¯Êýy=f£¨x£©µÄͼÏó¹ýµã$£¨2£¬2\sqrt{2}£©$£¬Ôòf£¨9£©=27£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

1£®ÒÑÖªx£¬y¡ÊR+£¬x+y=1£¬Ôò$\frac{x}{y}$+$\frac{1}{x}$µÄ×îСֵΪ3£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

18£®¹ýµã£¨1£¬1£©ÇÒ$\frac{b}{a}$=$\sqrt{2}$µÄË«ÇúÏߵıê×¼·½³ÌΪ£¨¡¡¡¡£©
A£®$\frac{{x}^{2}}{\frac{1}{2}}$-y2=1B£®$\frac{{y}^{2}}{\frac{1}{2}}$-x2=1
C£®x2-$\frac{{y}^{2}}{\frac{1}{2}}$=1D£®$\frac{{x}^{2}}{\frac{1}{2}}$-y2=1»ò$\frac{{y}^{2}}{\frac{1}{2}}$-x2=1

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

5£®ÓÐÏÂÁÐËĸöÃüÌ⣺
¢Ùy=2xÓëy=log2x»¥Îª·´º¯Êý£¬ÆäͼÏó¹ØÓÚÖ±Ïßy=x¶Ô³Æ£»
¢ÚÒÑÖªº¯Êýf£¨x-1£©=x2-2x+1£¬Ôòf£¨5£©=26£»
¢Ûµ±a£¾0ÇÒa¡Ù1ʱ£¬º¯Êýf£¨x£©=ax-2-3±Ø¹ý¶¨µã£¨2£¬-2£©£»
¢Üº¯Êýy=£¨$\frac{1}{2}$£©xµÄÖµÓòÊÇ£¨0£¬+¡Þ£©£®
ÄãÈÏΪÕýÈ·ÃüÌâµÄÐòºÅÊǢ٢ۢܣ¨°ÑÕýÈ·µÄÐòºÅ¶¼Ð´ÉÏ£©£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

15£®¸ø³öÏÂÁм¸¸ö˵·¨£º¢Ù¹ýÒ»µãÓÐÇÒÖ»ÓÐÒ»ÌõÖ±ÏßÓëÒÑÖªÖ±ÏßƽÐУ»¢Ú¹ýÒ»µãÓÐÇÒÖ»ÓÐÒ»ÌõÖ±ÏßÓëÒÑÖªÖ±Ïß´¹Ö±£»¢Û¹ýƽÃæÍâÒ»µãÓÐÇÒÖ»ÓÐÒ»ÌõÖ±ÏßÓë¸ÃƽÃæƽÐУ»¢Ü¹ýƽÃæÍâÒ»µãÓÐÇÒÖ»ÓÐÒ»¸öƽÃæÓë¸ÃƽÃæƽÐУ®ÆäÖÐÕýȷ˵·¨µÄ¸öÊýΪ£¨¡¡¡¡£©
A£®0B£®1C£®2D£®3

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

2£®Ò»ÌõÖ±ÏßÉÏ µÄÁ½µãÔÚÒ»¸öƽÃæÄÚ£¬ÄÇôÕâÌõÖ±Ïß¾ÍÔÚÕâ¸öƽÃæÄÚ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

19£®º¯Êýy=${x}^{-\frac{1}{3}}$ÊÇ£¨¡¡¡¡£©
A£®Æ溯ÊýB£®Å¼º¯Êý
C£®¼È²»ÊÇÆ溯Êý£¬Ò²²»ÊÇżº¯ÊýD£®¼ÈÊÇÆ溯Êý£¬Ò²ÊÇżº¯Êý

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

20£®ÒÑÖªÔ²P¹ýµãA£¨1£¬0£©£¬ÇÒÔ²ÐÄP£¨a£¬2£©£¨a¡Ù0£©µ½Ö±Ïßm£º4x-3y+1=0µÄ¾àÀëΪ1£¬ÒÔ×ø±êÔ­µãΪ¶Ô³ÆÖÐÐÄÇÒ½»µãÂäÔÚyÖáÉϵÄÍÖÔ²¦¸µÄÀëÐÄÂÊÓëÖ±Ïß2$\sqrt{2}$x-2y+3=0µÄбÂÊ»¥Îªµ¹Êý£¬¹ýµãA×÷Ò»Ìõ²»ÓëxÖá´¹Ö±µÄÖ±ÏßlÓëÍÖÔ²¦¸½»ÓÚC£¬DÁ½µã£®
£¨1£©ÇóÖ±Ïßm±»Ô²PËù½ØµÃµÄÏÒ³¤£»
£¨2£©ÈôB£¨4£¬0£©£¬xÖáǡΪ¡ÏCBDµÄ½Çƽ·ÖÏߣ¬ÇóÍÖÔ²¦¸µÄ±ê×¼·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸