ÒÑÖªÍÖÔ²C1£º
x2
a2
+
y2
b2
=1(a£¾b£¾0)
µÄÓÒ½¹µãÓëÅ×ÎïÏßC2£ºy2=4xµÄ½¹µãFÖغϣ¬µãMÊÇC1ÓëC2ÔÚµÚÒ»ÏóÏÞÄڵĽ»µã£¬ÇÒ|MF|=
5
3
£®
£¨1£©ÇóÍÖÔ²C1µÄ·½³Ì£»
£¨2£©ÉèÅ×ÎïÏßµÄ×¼ÏßÓëxÖá½»ÓÚµãE£¬¹ýEÈÎ×÷Ò»ÌõÖ±Ïßl£¬lÓëÍÖÔ²C1µÄÁ½¸ö½»µã¼ÇΪA£¬B£®ÎÊ£ºÔÚÍÖÔ²µÄ³¤ÖáÉÏÊÇ·ñ´æÔÚÒ»µãP£¬Ê¹
PA
PB
Ϊ¶¨Öµ£¿Èô´æÔÚ£¬Çó³öµãPµÄ×ø±ê¼°ÏàÓ¦µÄ¶¨Öµ£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®
·ÖÎö£º£¨1£©ÓÉÅ×ÎïÏߵĶ¨Òå½áºÏ|MF|=
5
3
Çó³öMµÄ×ø±ê£¬°ÑMµÄ×ø±ê´úÈëÍÖÔ²·½³Ì£¬½áºÏÒÑÖªÌõ¼þÇóµÃÍÖÔ²·½³Ì£»
£¨2£©Çó³öEµãµÄ×ø±ê£¬¼ÙÉè´æÔÚµãP£¨m£¬0£©£¨-2¡Üm¡Ü2£©Âú×ãÒªÇó£®Çó³öÖ±ÏßlµÄбÂʲ»´æÔÚºÍбÂÊΪ0ʱµÄ
PA
PB
Öµ£¬ÓÉÁ½ÖµÏàµÈÇó³ömµÄÖµ£¬È»ºó·ÖÇé¿öÖ¤Ã÷ËùÇóµÄPµã·ûºÏÒªÇó£®
½â´ð£º½â£º£¨1£©ÉèM£¨xM£¬yM£©£¬¡ßÅ×ÎïÏßC2£ºy2=4x£¬¡àÆä×¼Ïß·½³ÌΪx=-1£¬
ÓÉÅ×ÎïÏߵĶ¨ÒåµÃ£ºxM+1=
5
3
£¬µÃ£ºxM=
2
3
£¬´úÈëÅ×ÎïÏß·½³ÌµÃ£ºyM=
2
6
3
£¬
¡àM(
2
3
£¬
2
6
3
)
£®
½«´Ëµã´úÈëÍÖÔ²·½³Ì£¬µÃ
4
9a2
+
8
3b2
=1
£¬
ÓÖÍÖÔ²µÄ°ë½¹¾àc=1£¬a2=b2+c2£¬½âµÃ£ºa2=4£¬b2=3£®
¡àÍÖÔ²µÄ·½³ÌΪ£º
x2
4
+
y2
3
=1
£»
£¨2£©Å×ÎïÏßµÄ×¼ÏßÓëxÖá½»µãE£¨-1£¬0£©£¬¼ÙÉè´æÔÚµãP£¨m£¬0£©£¨-2¡Üm¡Ü2£©Âú×ãÒªÇó£®
µ±Ö±ÏßlµÄбÂʲ»´æÔÚʱ£¬ÇóµÃÁ½½»µãΪ(-1£¬
3
2
)£¬(-1£¬-
3
2
)
£¬´Ëʱ
PA
PB
=(-1-m)2-
9
4
£»
µ±Ö±ÏßlµÄбÂÊΪ0ʱ£¬ÇóµÃÁ½½»µãΪ£¨-2£¬0£©£¬£¨2£¬0£©£¬´Ëʱ
PA
PB
=(-2-m)(2-m)
£®
ÓÉ(-1-m)2-
9
4
=(-2-m)(2-m)
£¬½âµÃm=-
11
8
£®
ÏÂÃæÖ¤Ã÷P(-
11
8
£¬0)
·ûºÏÒªÇó£®
µ±Ö±ÏßlµÄбÂÊΪ0ʱ£¬
PA
PB
=m2-4=-
135
64
£®
µ±Ö±ÏßlµÄбÂʲ»Îª0ʱ£¬ÉèlµÄ·½³ÌΪx=ny-1£¬ÓÉ
x2
4
+
y2
3
=1
x=ny-1
µÃ£¬£¨3n2+4£©y2-6ny-9=0£®
ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬Ôòy1+y2=
6n
3n2+4
£¬y1y2=
-9
3n2+4
£®
´Ëʱ
PA
PB
=(x1+
11
8
)(x2+
11
8
)+y1y2=(ny1-1+
11
8
)(ny2-1+
11
8
)+y1y2

=
3n
8
(y1+y2)+(n2+1)y1y2+
9
64
=
-9(3n2+4)
4(3n2+4)
+
9
64
=-
135
64
£®
¹Ê´æÔÚµãP(-
11
8
£¬0)
·ûºÏÒªÇ󣬶ÔÓ¦µÄ¶¨ÖµÎª-
135
64
£®
µãÆÀ£º±¾Ì⿼²éÁËÍÖÔ²µÄ±ê×¼·½³ÌµÄÇ󷨣¬¿¼²éÁËÖ±ÏßÓëԲ׶ÇúÏßµÄλÖùØϵ£¬ÑµÁ·ÁËÉè¶ø²»ÇóµÄ½âÌâ˼Ïë·½·¨ºÍ·ÖÀàÌÖÂÛµÄÊýѧ˼Ïë·½·¨£¬ÑµÁ·ÁËÌØÖµÑéÖ¤·¨£¬¿¼²éÁËѧÉúÁé»î´¦ÀíÎÊÌâµÄÄÜÁ¦ºÍ¼ÆËãÄÜÁ¦£¬ÊǸ߿¼ÊÔ¾íÖеÄѹÖáÌ⣮
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÍÖÔ²C1£º
x2
a2
+
y2
b2
=1£¨a£¾b£¾0£©µÄ×ó¡¢ÓÒ½¹µã·Ö±ðΪF1¡¢F2£¬ÆäÖÐF2Ò²ÊÇÅ×ÎïÏßC2£ºy2=4xµÄ½¹µã£¬MÊÇC1ÓëC2ÔÚµÚÒ»ÏóÏ޵Ľ»µã£¬ÇÒ|MF2|=
5
3
£®
£¨1£©ÇóÍÖÔ²C1µÄ·½³Ì£»
£¨2£©ÒÑÖªÁâÐÎABCDµÄ¶¥µãA£¬CÔÚÍÖÔ²C1ÉÏ£¬¶Ô½ÇÏßBDËùÔÚµÄÖ±ÏßµÄбÂÊΪ1£®
¢Ùµ±Ö±ÏßBD¹ýµã£¨0£¬
1
7
£©Ê±£¬ÇóÖ±ÏßACµÄ·½³Ì£»
¢Úµ±¡ÏABC=60¡ãʱ£¬ÇóÁâÐÎABCDÃæ»ýµÄ×î´óÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

¾«Ó¢¼Ò½ÌÍøÒÑÖªÍÖÔ²C1£º
x2
a2
+
y2
b2
=1(a£¾b£¾0)
µÄÒ»Ìõ×¼Ïß·½³ÌÊÇx=
25
4
£¬Æä×ó¡¢ÓÒ¶¥µã·Ö±ðÊÇA¡¢B£»Ë«ÇúÏßC2£º
x2
a2
-
y2
b2
=1
µÄÒ»Ìõ½¥½üÏß·½³ÌΪ3x-5y=0£®
£¨1£©ÇóÍÖÔ²C1µÄ·½³Ì¼°Ë«ÇúÏßC2µÄÀëÐÄÂÊ£»
£¨2£©ÔÚµÚÒ»ÏóÏÞÄÚÈ¡Ë«ÇúÏßC2ÉÏÒ»µãP£¬Á¬½ÓAP½»ÍÖÔ²C1ÓÚµãM£¬Á¬½ÓPB²¢ÑÓ³¤½»ÍÖÔ²C1ÓÚµãN£¬Èô
AM
=
MP
£®Çó
MN
AB
µÄÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÍÖÔ²C1£º
x2
a2
+
y2
b2
=1(a£¾b£¾0)
µÄÀëÐÄÂÊΪ
2
2
£¬Ö±Ïßl£ºy=x+2
2
ÓëÒÔÔ­µãΪԲÐÄ¡¢ÒÔÍÖÔ²C1µÄ¶Ì°ëÖ᳤Ϊ°ë¾¶µÄÔ²ÏàÇУ®
£¨¢ñ£©ÇóÍÖÔ²C1µÄ·½³Ì£®
£¨¢ò£©ÉèÍÖÔ²C1µÄ×ó½¹µãΪF1£¬ÓÒ½¹µãΪF2£¬Ö±Ïßl1¹ýµãF1£¬ÇÒ´¹Ö±ÓÚÍÖÔ²µÄ³¤Öᣬ¶¯Ö±Ïßl2´¹Ö±l1ÓÚµãP£¬Ï߶ÎPF2µÄ´¹Ö±Æ½·ÖÏß½»l2ÓÚµãM£¬ÇóµãMµÄ¹ì¼£C2µÄ·½³Ì£»
£¨¢ó£©ÈôAC¡¢BDΪÍÖÔ²C1µÄÁ½ÌõÏ໥´¹Ö±µÄÏÒ£¬´¹×ãΪÓÒ½¹µãF2£¬ÇóËıßÐÎABCDµÄÃæ»ýµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÍÖÔ²C1£º
x2
a2
+
y2
b2
=1£¨a£¾b£¾0£©ÓëË«ÇúÏßC2£ºx2-
y2
4
=1Óй«¹²µÄ½¹µã£¬C2µÄÒ»Ìõ½¥½üÏßÓëÒÔC1µÄ³¤ÖáΪֱ¾¶µÄÔ²ÏཻÓÚA£¬BÁ½µã£¬ÈôC1Ç¡ºÃ½«Ï߶ÎABÈýµÈ·Ö£¬Ôòb2=
0.5
0.5
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2013•ÉÇͷһģ£©ÒÑÖªÍÖÔ²C1£º
x2
a2
+
y2
b2
=1(a£¾b£¾0)
µÄ×ó¡¢ÓÒ½¹µã·Ö±ðΪF1¡¢F2£¬ÓÒ¶¥µãΪA£¬ÀëÐÄÂÊe=
1
2

£¨1£©ÉèÅ×ÎïÏßC2£ºy2=4xµÄ×¼ÏßÓëxÖá½»ÓÚF1£¬ÇóÍÖÔ²µÄ·½³Ì£»
£¨2£©ÉèÒÑ֪˫ÇúÏßC3ÒÔÍÖÔ²C1µÄ½¹µãΪ¶¥µã£¬¶¥µãΪ½¹µã£¬bÊÇË«ÇúÏßC3ÔÚµÚÒ»ÏóÏÞÉÏÈÎÒâ-µã£¬ÎÊÊÇ·ñ´æÔÚ³£Êý¦Ë£¨¦Ë£¾0£©£¬Ê¹¡ÏBAF1=¦Ë¡ÏBF1Aºã³ÉÁ¢£¿Èô´æÔÚ£¬Çó³ö¦ËµÄÖµ£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸