5£®ÒÑÖªÍÖÔ²$\frac{x^2}{a^2}$+$\frac{y^2}{b^2}$=1£¨a£¾b£¾0£©£¬¾­¹ýÍÖÔ²CÉÏÒ»µãPµÄÖ±Ïßl£ºy=-$\frac{{\sqrt{2}}}{4}$x+$\frac{{3\sqrt{2}}}{2}$ÓëÍÖÔ²CÓÐÇÒÖ»ÓÐÒ»¸ö¹«¹²µã£¬ÇÒµãPºá×ø±êΪ2£®
£¨¢ñ£©ÇóÍÖÔ²CµÄ±ê×¼·½³Ì£»
£¨¢ò£©ÈôABÊÇÍÖÔ²µÄÒ»Ìõ¶¯ÏÒ£¬ÇÒ|AB|=$\frac{5}{2}$£¬OÎª×ø±êÔ­µã£¬Çó¡÷AOBÃæ»ýµÄ×î´óÖµ£®

·ÖÎö £¨¢ñ£©ÓÉpµÄºá×ø±ê¿ÉµÃPµÄ×ø±ê£¬´úÈëÍÖÔ²·½³Ì£¬ÁªÁ¢Ö±Ïß·½³ÌºÍÍÖÔ²·½³Ì£¬»¯Îª¹ØÓÚxµÄÒ»Ôª¶þ´Î·½³Ì£¬ÓÉÅбðʽµÈÓÚ0µÃµ½a£¬b¹ØÏµ£¬½øÒ»²½ÇóµÃa£¬bµÄÖµ£¬ÔòÍÖÔ²CµÄ±ê×¼·½³Ì¿ÉÇó£»
£¨¢ò£©ÉèÖ±ÏßAB·½³ÌΪ£ºy=kx+b£¬ÁªÁ¢Ö±Ïß·½³ÌºÍÍÖÔ²·½³Ì£¬ÀûÓÃÏÒ³¤¹«Ê½ÇóµÃk¡¢bµÄ¹ØÏµ£¬Çó³öÔ­µãOµ½Ö±ÏßABµÄ¾àÀ룬°Ñ¡÷AOBµÄÃæ»ý»¯Îªº¬ÓÐkµÄº¯Êý£¬È»ºóÀûÓû»Ôª·¨ÇóµÃ×îÖµ£®

½â´ð ½â£º£¨¢ñ£©¡ßP£¨2£¬$\sqrt{2}$£©£¬¡à$\frac{4}{{a}^{2}}+\frac{2}{{b}^{2}}=1$£¬¢Ù
ÁªÁ¢$\left\{\begin{array}{l}{{b}^{2}{x}^{2}+{a}^{2}{y}^{2}={a}^{2}{b}^{2}}\\{y=-\frac{\sqrt{2}}{4}x+\frac{3}{2}\sqrt{2}}\end{array}\right.$£¬µÃ${b}^{2}{x}^{2}+{a}^{2}£¨-\frac{\sqrt{2}}{4}x+\frac{3\sqrt{2}}{2}£©^{2}={a}^{2}{b}^{2}$£¬
»¯¼òµÃ£º$£¨{b}^{2}+\frac{1}{8}{a}^{2}£©{x}^{2}-$$\frac{3}{2}{a}^{2}x+\frac{9}{2}{a}^{2}-{a}^{2}{b}^{2}=0$£®
ÓÉ¡÷=$\frac{9}{4}{a}^{4}-4£¨{b}^{2}+\frac{1}{8}{a}^{2}£©£¨\frac{9}{2}{a}^{2}-{a}^{2}{b}^{2}£©=0$£¬¢Ú
ÁªÁ¢¢Ù¢ÚµÃ£ºa2=12£¬b2=3£¬
¡àÍÖÔ²·½³ÌΪ$\frac{{x}^{2}}{12}+\frac{{y}^{2}}{3}=1$£»
£¨¢ò£©ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬Ö±ÏßAB·½³ÌΪ£ºy=kx+b£¬
ÁªÁ¢$\left\{\begin{array}{l}{{x}^{2}+4{y}^{2}=12}\\{y=kx+b}\end{array}\right.$£¬µÃ£¨4k2+1£©x2+8kbx+4£¨b2-3£©=0£®
¹Ê${x}_{1}+{x}_{2}=-\frac{8kb}{1+4{k}^{2}}£¬{x}_{1}{x}_{2}=\frac{4£¨{b}^{2}-3£©}{1+4{k}^{2}}$£¬
ÓÉ$\frac{25}{4}=|AB{|}^{2}=£¨1+{k}^{2}£©£¨{x}_{2}-{x}_{1}£©^{2}=£¨1+{k}^{2}£©$$[£¨{x}_{1}+{x}_{2}£©^{2}-4{x}_{1}{x}_{2}]$£¬
µÃ${b}^{2}=3£¨1+4{k}^{2}£©-\frac{25£¨1+4{k}^{2}£©^{2}}{64£¨1+{k}^{2}£©}$£¬
¹ÊÔ­µãOµ½Ö±ÏßABµÄ¾àÀëd=$\frac{|b|}{\sqrt{1+{k}^{2}}}$£¬¡àS=$\frac{5}{4}•\frac{|b|}{\sqrt{1+{k}^{2}}}$£¬
Áîu=$\frac{1+4{k}^{2}}{1+{k}^{2}}$£¬Ôò${S}^{2}=-\frac{625}{1024}£¨{u}^{2}-\frac{192}{25}u£©=-\frac{625}{1024}£¨u-\frac{96}{25}£©^{2}+9$£®
ÓÖ¡ß$u=\frac{1+4{k}^{2}}{1+{k}^{2}}=4-\frac{3}{1+{k}^{2}}$¡Ê[1£¬4£©£¬µ±u=$\frac{96}{25}$ʱ£¬S2max=9£»
µ±Ð±Âʲ»´æÔÚʱ£¬¡÷AOBÃæ»ýµÄ×î´óֵΪ$\frac{5\sqrt{23}}{8}$£®
×ÛÉÏ¿ÉÖª£¬¡÷AOBÃæ»ýµÄ×î´óֵΪ3£®

µãÆÀ ±¾Ì⿼²éÍÖÔ²µÄ¼òµ¥ÐÔÖÊ£¬¿¼²éÁËÖ±ÏßÓëÍÖԲλÖùØÏµµÄÓ¦Óã¬ÑµÁ·ÁË»»Ôª·¨Çóº¯ÊýµÄ×îÖµ£¬ÊÇÖеµÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

15£®ÒÑÖª£ºsinx+siny+sinz=cosx+cosy+cosz=0£¬ÇóS=tan£¨x+y+z£©+tanxtanytanzµÄÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

16£®£¨1£©Èôf£¨x+$\frac{1}{x}$£©=x2+$\frac{1}{{x}^{2}}$£¬Ôòf£¨x£©=x2-2£®
£¨2£©Èôf£¨2x-1£©=x2+x£¬Ôòf£¨x£©=$\frac{1}{4}{x}^{2}+x+\frac{3}{4}$£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

13£®ÔÚËÄÀâ×¶P-ABCDÖУ¬¶¥µãΪP£¬´ÓÆäËüµÄ¶¥µãºÍ¸÷ÀâµÄÖеãÖÐÈ¡3¸ö£¬Ê¹ËüÃǺ͵ãPÔÚÍ¬Ò»Æ½ÃæÄÚ£¬²»Í¬µÄÈ¡·¨ÓУ¨¡¡¡¡£©
A£®40B£®48C£®56D£®62

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

20£®ÒÑÖªÆ½ÃæÏòÁ¿$\overrightarrow{p}$=£¨mlnx+ln2e2£¬x£©£¬$\overrightarrow{q}$=£¨1£¬$\frac{x}{2}$-m-1£©£¬º¯Êýf£¨x£©=$\overrightarrow{p}$•$\overrightarrow{q}$£¨ÆäÖÐe=2.71828¡­ÊÇ×ÔÈ»¶ÔÊýµÄµ×Êý£©£®
£¨1£©µ±m=-1ʱ£¬Çóº¯Êýf£¨x£©ÔÚµãP£¨2£¬f£¨2£©£©´¦µÄÇÐÏß·½³Ì£»
£¨2£©ÌÖÂÛº¯Êýf£¨x£©µÄ¼«ÖµÇé¿ö£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

10£®ÒÑÖªº¯Êýf£¨x£©=|2x-1|+|x+1|£®
£¨1£©½â²»µÈʽf£¨x£©£¼4£»
£¨2£©Èô´æÔÚʵÊýx0£¬Ê¹µÃf£¨x0£©£¼log2$\sqrt{{t}^{2}-1}$³ÉÁ¢£¬ÇóʵÊýtµÄȡֵ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

17£®ÔËÐÐÈçͼËùʾµÄÁ÷³Ìͼ£¬ÔòÊä³öµÄ½á¹ûanÊÇ£¨¡¡¡¡£©
A£®-5B£®-4C£®-1D£®1

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

4£®ÒÑÖªÖ±Ïßl1£ºax+£¨a+2£©y+1=0£¬l2£ºax-y+2=0£®Ôò¡°a=-3¡±ÊÇ¡°l1¡Îl2¡±µÄ³ä·Ö²»±ØÒªÌõ¼þ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

5£®Èçͼ£¬Ð´³öÖÕ±ßÂäÔÚÒõÓ°²¿·ÖµÄ½Ç¦ÁµÄ¼¯ºÏ£¨º¬±ß½ç£©{¦Á|k•360¡ã¡Ü¦Á¡Ü45¡ã+k•360¡ã£¬k¡ÊZ}£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸