1£®ÒÑÖªÍÖÔ²C£º$\frac{{x}^{2}}{{a}^{2}}$+$\frac{{y}^{2}}{{b}^{2}}$=1£¨a£¾b£¾0£©µÄÀëÐÄÂÊe=$\frac{\sqrt{2}}{2}$£¬ÇÒÍÖÔ²ÉÏÒ»µãMÓëÍÖÔ²×óÓÒÁ½¸ö½¹µã¹¹³ÉµÄÈý½ÇÐÎÖܳ¤Îª4+2$\sqrt{2}$£®
£¨1£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨2£©Èçͼ£¬ÉèµãDΪÍÖÔ²ÉÏÈÎÒâÒ»µã£¬Ö±Ïßy=mºÍÍÖÔ²C½»ÓÚA¡¢BÁ½µã£¬ÇÒÖ±ÏßDA¡¢DBÓëyÖá·Ö±ð½»ÓÚP¡¢QÁ½µã£¬ÊÔ̽¾¿¡ÏPF1F2ºÍ¡ÏQF1F2Ö®¼äµÄµÈÁ¿¹ØÏµ²¢¼ÓÒÔÖ¤Ã÷£®

·ÖÎö £¨1£©£ºÓÉÌâÒâ¿ÉµÃ£ºe=$\frac{\sqrt{2}}{2}$=$\frac{c}{a}$£¬2a+2c=4+2$\sqrt{2}$£¬ÓÖa2=b2+c2£®ÁªÁ¢½â³ö¼´¿ÉµÃ³öÍÖÔ²CµÄ·½³Ì£®
£¨2£©ÉèD£¨x0£¬y0£©£¬Ôò$\frac{{x}_{0}^{2}}{4}$+$\frac{{y}_{0}^{2}}{2}$=1£®°Ñy=m´úÈëÍÖÔ²·½³Ì¿ÉµÃ£ºA£¨-$\sqrt{4-2{m}^{2}}$£¬m£©£¬B£¨$\sqrt{4-2{m}^{2}}$£¬m£©£®ÀûÓõãбʽ¿ÉµÃ£ºÖ±ÏßDAµÄ·½³ÌÓëÖ±ÏßDBµÄ·½³Ì£¬¿ÉµÃP£¬QµÄ×ø±ê£®ÀûÓÃбÂʹ«Ê½Ö»ÒªÖ¤Ã÷${k}_{P{F}_{1}}$•${k}_{Q{F}_{1}}$=1¼´¿ÉµÃ³ö£®

½â´ð £¨1£©½â£ºÓÉÌâÒâ¿ÉµÃ£ºe=$\frac{\sqrt{2}}{2}$=$\frac{c}{a}$£¬2a+2c=4+2$\sqrt{2}$£¬ÓÖa2=b2+c2£®
ÁªÁ¢½âµÃ£ºa=2£¬b=c=$\sqrt{2}$£®
¡àÍÖÔ²CµÄ·½³ÌΪ£º$\frac{{x}^{2}}{4}+\frac{{y}^{2}}{2}$=1£®
£¨2£©½â£º¡ÏPF1F2+¡ÏQF1F2=90¡ã£®
ÏÂÃæ¸ø³öÖ¤Ã÷£ºF1$£¨-\sqrt{2}£¬0£©$£®
ÉèD£¨x0£¬y0£©£¬Ôò$\frac{{x}_{0}^{2}}{4}$+$\frac{{y}_{0}^{2}}{2}$=1£®
°Ñy=m´úÈëÍÖÔ²·½³Ì¿ÉµÃ£º$\frac{{x}^{2}}{4}$+$\frac{{m}^{2}}{2}$=1£¬½âµÃx=¡À$\sqrt{4-2{m}^{2}}$£®
È¡A£¨-$\sqrt{4-2{m}^{2}}$£¬m£©£¬B£¨$\sqrt{4-2{m}^{2}}$£¬m£©£®
Ö±ÏßDAµÄ·½³ÌΪ£ºy-y0=$\frac{m-{y}_{0}}{-\sqrt{4-2{m}^{2}}-{x}_{0}}$£¨x-x0£©£¬¿ÉµÃP$£¨0£¬\frac{£¨m-{y}_{0}£©{x}_{0}}{\sqrt{4-2{m}^{2}}+{x}_{0}}+{y}_{0}£©$£®
ͬÀí¿ÉµÃ£ºÖ±ÏßDBµÄ·½³ÌΪ£ºy-y0=$\frac{m-{y}_{0}}{\sqrt{4-2{m}^{2}}-{x}_{0}}$£¨x-x0£©£¬¿ÉµÃQ$£¨0£¬\frac{-{x}_{0}£¨m-{y}_{0}£©}{\sqrt{4-2{m}^{2}}-{x}_{0}}+{y}_{0}£©$£®
¡à${k}_{P{F}_{1}}$=$\frac{m{x}_{0}+{y}_{0}\sqrt{4-2{m}^{2}}}{\sqrt{2}£¨\sqrt{4-2{m}^{2}}+{x}_{0}£©}$£¬
${k}_{Q{F}_{1}}$=$\frac{-m{x}_{0}+{y}_{0}\sqrt{4-2{m}^{2}}}{\sqrt{2}£¨\sqrt{4-2{m}^{2}}-{x}_{0}£©}$£®
ÓÖ${y}_{0}^{2}$=2-$\frac{{x}_{0}^{2}}{2}$£®
¡à${k}_{P{F}_{1}}$•${k}_{Q{F}_{1}}$=$\frac{m{x}_{0}+{y}_{0}\sqrt{4-2{m}^{2}}}{\sqrt{2}£¨\sqrt{4-2{m}^{2}}+{x}_{0}£©}$•$\frac{-m{x}_{0}+{y}_{0}\sqrt{4-2{m}^{2}}}{\sqrt{2}£¨\sqrt{4-2{m}^{2}}-{x}_{0}£©}$=$\frac{{y}_{0}^{2}£¨4-2{m}^{2}£©-{m}^{2}{x}_{0}^{2}}{2£¨4-2{m}^{2}-{x}_{0}^{2}£©}$=$\frac{£¨2-\frac{{x}_{0}^{2}}{2}£©£¨4-2{m}^{2}£©-{m}^{2}{x}_{0}^{2}}{2£¨4-2{m}^{2}-{x}_{0}^{2}£©}$=1£®
¡à¡ÏPF1F2+¡ÏQF1F2=90¡ã£®

µãÆÀ ±¾Ì⿼²éÁËÍÖÔ²µÄ±ê×¼·½³Ì¼°ÆäÐÔÖÊ¡¢Ö±ÏßÓëÍÖÔ²ÏཻÎÊÌâ¡¢Ö±Ïß·½³Ì¡¢Ð±ÂʼÆË㹫ʽ¡¢µãÓëÍÖÔ²µÄλÖùØÏµ£¬¿¼²éÁË̽¾¿ÄÜÁ¦¡¢ÍÆÀíÄÜÁ¦Óë¼ÆËãÄÜÁ¦£¬ÊôÓÚÄÑÌ⣮

Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÌî¿ÕÌâ

11£®Ö±Ïßx=$\frac{¦Ð}{2}$£¬x=$\frac{3¦Ð}{2}$£¬y=0¼°ÇúÏßy=cosxËùΧ³ÉͼÐεÄÃæ»ýΪ2£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

12£®ÒÔ×ø±êÔ­µãΪ¼«µã£¬xÖáµÄÕý°ëÖáΪ¼«ÖὨÁ¢¼«×ø±êϵ£¬Á½×ø±êϵȡÏàͬµ¥Î»£¬ÒÑÖªÇúÏßC1µÄ¼«×ø±ê·½³ÌΪ¦Ñ2-4¦Ñcos¦È=0£¬ÒÑÖªµãAµÄ¼«×ø±êΪ£¨3$\sqrt{2}$£¬$\frac{¦Ð}{4}$£©£¬Ö±ÏßlµÄ¼«×ø±ê·½³ÌΪ¦Ñcos£¨¦È-$\frac{¦Ð}{4}$£©=a£¬ÇÒµãAÔÚÖ±ÏßlÉÏ£®
£¨1£©°ÑÇúÏßC1µÄ¼«×ø±ê·½³Ì»¯Îª²ÎÊý·½³Ì£»
£¨2£©ÇóÇúÏßC1ÉÏÈÎÒâÒ»µãµ½Ö±ÏßlµÄ¾àÀëµÄ×î´óÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

9£®Èçͼ£¬ÔÚËÄÀâÖùP-ABCDÖУ¬µ×ÃæABCDÊǾØÐΣ¬EÊÇÀâPAµÄÖе㣬PD¡ÍAD£®
£¨¢ñ£©ÇóÖ¤£ºPC¡ÎÆ½ÃæBED£»
£¨¢ò£©ÈôCD=1£¬BC=PC=PD=2£¬ÇóÈýÀâ×¶P-BCDµÄÌå»ý£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

16£®ÍÖÔ²$\frac{x^2}{4}$+$\frac{y^2}{3}$=1µÄ³¤ÖáΪA1A2£¬¶ÌÖáΪB1B2£¬½«×ø±êÆ½ÃæÑØyÖáÕÛ³ÉÒ»¸ö¶þÃæ½Ç£¬Ê¹A1µãÔÚÆ½ÃæB1A2B2ÉϵÄÉäÓ°Ç¡ºÃÊǸÃÍÖÔ²µÄÓÒ½¹µã£¬Ôò´Ë¶þÃæ½ÇµÄ´óСΪ£¨¡¡¡¡£©
A£®30¡ãB£®45¡ãC£®60¡ãD£®75¡ã

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

6£®ÒÑÖªº¯Êýf£¨x£©=sin£¨2¦Øx-$\frac{¦Ð}{6}}$£©-4sin2¦Øx+2£¨{¦Ø£¾0}£©£¬ÆäͼÏóÓëxÖáÏàÁÚµÄÁ½¸ö½»µãµÄ¾àÀëΪ$\frac{¦Ð}{2}$£®
£¨I£©Çóº¯ÊýµÄf£¨x£©½âÎöʽ£»
£¨¢ò£©Èô½«f£¨x£©µÄͼÏóÏò×óÆ½ÒÆm£¨m£¾0£©¸ö³¤¶Èµ¥Î»µÃµ½º¯Êýg£¨x£©µÄͼÏóÇ¡ºÃ¾­¹ýµã£¨${-\frac{¦Ð}{3}$£¬0£©£¬Çóµ±mÈ¡µÃ×îСֵʱ£¬g£¨x£©ÔÚ[${-\frac{¦Ð}{6}$£¬$\frac{7¦Ð}{12}}$]Éϵĵ¥µ÷Çø¼ä£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

13£®ÒÑÖªÍÖÔ²CµÄÖÐÐÄÔÚÔ­µã£¬½¹µãÔÚxÖáÉÏ£¬ÀëÐÄÂÊΪ$\frac{1}{2}$£¬ËüµÄÒ»¸ö¶¥µãÇ¡ºÃÊÇÅ×ÎïÏßx2=8$\sqrt{3}$yµÄ½¹µã£®
£¨I£©ÇóÍÖÔ²C±ê×¼·½³Ì£»
£¨¢ò£©Ö±Ïßx=2£¬ÓëÍÖÔ²½»ÓÚP£¬QÁ½µã£¬A£¬BÊÇÍÖÔ²ÉÏλÓÚÖ±Ïßx=2Á½²àµÄ¶¯µã£¬ÈôÖ±ÏßABµÄбÂÊΪ$\frac{1}{2}$£¬ÇóËıßÐÎAPBQÃæ»ýµÄ×î´óÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£ºÑ¡ÔñÌâ

10£®ÒÑ֪ȫ¼¯U=R£¬N={x|$\frac{1}{8}$£¼2x£¼1}£¬M={x|y=ln£¨-x-1£©}£¬ÔòͼÖÐÒõÓ°²¿·Ö±íʾµÄ¼¯ºÏÊÇ£¨¡¡¡¡£©
A£®{x|-3£¼x£¼-1}B£®{x|-3£¼x£¼0}C£®{x|-1¡Üx£¼0}D£®{x|x£¼-3}

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º½â´ðÌâ

11£®Ò»¸öµÈ±ÈÊýÁеĵÚ9ÏîÊÇ$\frac{4}{9}$£¬¹«±ÈÊÇ-$\frac{1}{3}$£®ÇóËüµÄµÚ1Ï

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸