Èçͼ£¬ÒÑÖªÍÖÔ²C£º
x2
a2
+
y2
b2
=1(a£¾b£¾0)
µÄÀëÐÄÂÊÊÇ
2
2
£¬A1£¬A2·Ö±ðÊÇÍÖÔ²CµÄ×ó¡¢ÓÒÁ½¸ö¶¥µã£¬µãFÊÇÍÖÔ²CµÄÓÒ½¹µã£®µãDÊÇxÖáÉÏλÓÚA2ÓÒ²àµÄÒ»µã£¬ÇÒÂú×ã
1
|A1D|
+
1
|A2D|
=
2
|FD|
=2
£®
£¨1£©ÇóÍÖÔ²CµÄ·½³ÌÒÔ¼°µãDµÄ×ø±ê£»
£¨2£©¹ýµãD×÷xÖáµÄ´¹Ïßn£¬ÔÙ×÷Ö±Ïßl£ºy=kx+mÓëÍÖÔ²CÓÐÇÒ½öÓÐÒ»¸ö¹«¹²µãP£¬Ö±Ïßl½»Ö±ÏßnÓÚµãQ£®ÇóÖ¤£ºÒÔÏ߶ÎPQΪֱ¾¶µÄÔ²ºã¹ý¶¨µã£¬²¢Çó³ö¶¨µãµÄ×ø±ê£®
£¨1£©A1£¨-a£¬0£©£¬A2£¨a£¬0£©£¬F£¨c£¬0£©£¬ÉèD£¨x£¬0£©£¬
ÓÉ
1
|A1D|
+
1
|A2D|
=2
ÓÐ
1
x+a
+
1
x-a
=2
£¬
ÓÖ|FD|=1£¬¡àx-c=1£¬¡àx=c+1£¬
ÓÚÊÇ
1
c+1+a
+
1
c+1-a
=2
£¬
¡àc+1=£¨c+1+a£©£¨c+1-a£©£¬
ÓÖ¡ß
c
a
=
2
2
⇒a=
2
c
£¬¡àc+1=(c+1+
2
c)(c+1-
2
c)
£¬
¡àc2-c=0£¬ÓÖc£¾0£¬¡àc=1£¬
¡àa=
2
£¬b=1
£¬
¡àÍÖÔ²C£º
x2
2
+y2=1
£¬ÇÒD£¨2£¬0£©£®
£¨2£©Ö¤Ã÷£º¡ßQ£¨2£¬2k+m£©£¬ÉèP£¨x0£¬y0£©£¬
ÓÉ
y=kx+m
x2
2
+y2=1
x2
2
+(kx+m)2=1
⇒x2+2£¨kx+m£©2=2⇒£¨2k2+1£©x2+4kmx+2m2-2=0£¬
ÓÉÓÚ¡÷=16k2m2-4£¨2k2+1£©£¨2m2-2£©=0⇒2k2-m2+1=0⇒m2=2k2+1£¨*£©£¬
¶øÓÉΤ´ï¶¨Àí£º2x0=
-4km
2k2+1
£¬
¡àx0=
-2km
2k2+1
£¬
ÓÉ£¨*£©¿ÉµÃ
-2km
m2
=-
2k
m
£¬¡ày0=kx0+m=-
2k2
m
+m=
1
m
£¬¡àP(-
2k
m
£¬
1
m
)
£¬
ÉèÒÔÏ߶ÎPQΪֱ¾¶µÄÔ²ÉÏÈÎÒâÒ»µãM£¨x£¬y£©£¬
ÓÉ
MP
MQ
=0
ÓÐ(x+
2k
m
)(x-2)+(y-
1
m
)(y-(2k+m))=0⇒x2+y2+(
2k
m
-2)x+(2k+m+
1
m
)y+(1-
2k
m
)=0
£¬
ÓɶԳÆÐÔÖª¶¨µãÔÚxÖáÉÏ£¬Áîy=0£¬È¡AʱÂú×ãÉÏʽ£¬¹Ê¹ý¶¨µãC£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º²»Ïê ÌâÐÍ£º½â´ðÌâ

ÒÑÖªÍÖÔ²CµÄÖÐÐÄÔÚ×ø±êÔ­µãO£¬×󶥵ãA£¨-2£¬0£©£¬ÀëÐÄÂÊe=
1
2
£¬FΪÓÒ½¹µã£¬¹ý½¹µãFµÄÖ±Ïß½»ÍÖÔ²CÓÚP¡¢QÁ½µã£¨²»Í¬ÓÚµãA£©£®
£¨¢ñ£©ÇóÍÖÔ²CµÄ·½³Ì£»
£¨¢ò£©µ±¡÷APQµÄÃæ»ýS=
18
2
7
ʱ£¬ÇóÖ±ÏßPQµÄ·½³Ì£»
£¨¢ó£©Çó
OP
FP
µÄ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º²»Ïê ÌâÐÍ£º½â´ðÌâ

Çó¾­¹ýµãP£¨-1£¬-6£©ÓëÅ×ÎïÏßC£ºx2=4yÖ»ÓÐÒ»¸ö¹«¹²µãµÄÖ±Ïßl·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º²»Ïê ÌâÐÍ£º½â´ðÌâ

Èçͼ£¬ÍÖÔ²C1£º
x2
a2
+
y2
b2
=1£¨a£¾b£¬b£¾0£©ºÍÔ²C2£ºx2+y2=b2£¬ÒÑÖªÔ²C2½«ÍÖÔ²ClµÄ³¤ÖáÈýµÈ·Ö£¬ÇÒÔ²C2µÄÃæ»ýΪ¦Ð£®ÍÖÔ²ClµÄ϶¥µãΪE£¬¹ý×ø±êÔ­µãOÇÒÓë×ø±êÖá²»ÖغϵÄÈÎÒâÖ±ÏßlÓëÔ²C2ÏཻÓÚµãA¡¢B£¬Ö±ÏßEA¡¢EBÓëÍÖÔ²C1µÄÁíÒ»¸ö½»µã·Ö±ðÊǵãP¡¢M£®
£¨¢ñ£©ÇóÍÖÔ²C1µÄ·½³Ì£»
£¨¢ò£©£¨i£©ÉèPMµÄбÂÊΪt£¬Ö±ÏßlбÂÊΪK1£¬Çó
K1
t
掙术
£¨ii£©Çó¡÷EPMÃæ»ý×î´óʱֱÏßlµÄ·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º²»Ïê ÌâÐÍ£ºÌî¿ÕÌâ

µãPÔÚÖ±Ïßl£ºy=x-1ÉÏ£¬Èô´æÔÚ¹ýPµÄÖ±Ïß½»Å×ÎïÏßy=x2ÓÚA£¬BÁ½µã£¬ÇÒ
PA
=
AB
£¬Ôò³ÆµãPΪ¡°¦Ëµã¡±£¬ÄÇôֱÏßlÉÏÓÐ______¸ö¡°¦Ëµã¡±£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º²»Ïê ÌâÐÍ£º½â´ðÌâ

ÒÑ֪ƽÃæÄÚÒ»¶¯µãPµ½µãF£¨2£¬0£©µÄ¾àÀë±ÈµãPµ½yÖáµÄ¾àÀë´ó2£¬
£¨¢ñ£©Ç󶯵ãPµÄ¹ì¼£CµÄ·½³Ì£»
£¨¢ò£©¹ýµãFÇÒбÂÊΪ2
2
µÄÖ±Ïß½»¹ì¼£CÓÚA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¨x1£¼x2£©Á½µã£¬P£¨x3£¬y3£©£¨x3¡Ý0£©Îª¹ì¼£CÉÏÒ»µã£¬Èô
OP
=
OA
+¦Ë
OB
£¬Çó¦ËµÄÖµ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º²»Ïê ÌâÐÍ£º½â´ðÌâ

Å×ÎïÏßC£ºy2=2px£¨p£¾0£©µÄ½¹µãΪF£¬Å×ÎïÏßCÉϵãMµÄºá×ø±êΪ2£¬ÇÒ|MF|=3£®
£¨1£©ÇóÅ×ÎïÏßCµÄ·½³Ì£»
£¨2£©¹ý½¹µãF×÷Á½ÌõÏ໥´¹Ö±µÄÖ±Ïߣ¬·Ö±ðÓëÅ×ÎïÏßC½»ÓÚM¡¢NºÍP¡¢QËĵ㣬ÇóËıßÐÎMPNQÃæ»ýµÄ×îСֵ£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º²»Ïê ÌâÐÍ£º½â´ðÌâ

ÒÑÖªÍÖÔ²C1µÄ·½³ÌΪ
x2
4
+y2=1£¬Ë«ÇúÏßC2µÄ×ó¡¢ÓÒ½¹µã·Ö±ðΪC1µÄ×ó¡¢ÓÒ¶¥µã£¬¶øC2µÄ×ó¡¢ÓÒ¶¥µã·Ö±ðÊÇC1µÄ×ó¡¢ÓÒ½¹µã£®
£¨¢ñ£©ÇóË«ÇúÏßC2µÄ·½³Ì£»
£¨¢ò£©ÈôÖ±Ïßl£ºy=kx+
2
ÓëÍÖÔ²C1¼°Ë«ÇúÏßC2¶¼ºãÓÐÁ½¸ö²»Í¬µÄ½»µã£¬ÇÒlÓëC2µÄÁ½¸ö½»µãAºÍBÂú×ã
OA
OB
£¼6£¨ÆäÖÐOΪԭµã£©£¬ÇókµÄÈ¡Öµ·¶Î§£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º²»Ïê ÌâÐÍ£º½â´ðÌâ

ÒÑ֪˫ÇúÏßC£º
x2
a2
-
y2
b2
=1(a£¾0£¬b£¾0)
£¬Ö±Ïßl£ºy=
3
(x-4)
¹ØÓÚÖ±Ïßl1£ºy=
b
a
x
¶Ô³ÆµÄÖ±Ïßl¡äÓëxÖáƽÐУ®
£¨1£©ÇóË«ÇúÏßµÄÀëÐÄÂÊ£»
£¨2£©ÈôµãM£¨4£¬0£©µ½Ë«ÇúÏßÉϵĵãPµÄ×îС¾àÀëµÈÓÚ1£¬ÇóË«ÇúÏߵķ½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸