ÌâÄ¿ÄÚÈÝ
ÒÑÖªÍÖÔ²
+
=1(a£¾b£¾0)µÄ×ó¡¢ÓÒ½¹µã·Ö±ðÊÇF1£¨-c£¬0£©¡¢F2£¨c£¬0£©£¬QÊÇÍÖÔ²ÍâµÄ¶¯µã£¬Âú×ã|
|=2a£®µãPÊÇÏ߶ÎF1QÓë¸ÃÍÖÔ²µÄ½»µã£¬µãTÔÚÏ߶ÎF2QÉÏ£¬²¢ÇÒÂú×ã
•
=0£¬|
|¡Ù0£®
£¨1£©ÇóÖ¤£º|PQ|=|PF2|£»
£¨2£©ÇóµãTµÄ¹ì¼£CµÄ·½³Ì£»
£¨3£©ÈôÍÖÔ²µÄÀëÐÄÂÊe=
£¬ÊÔÅжϹ켣CÉÏÊÇ·ñ´æÔÚµãM£¬Ê¹¡÷F1MF2µÄÃæ»ýS=b2£¬Èô´æÔÚ£¬ÇëÇó³ö¡ÏF1MF2µÄÕýÇÐÖµ£®
x2 |
a2 |
y2 |
b2 |
F1Q |
PT |
TF2 |
TF2 |
£¨1£©ÇóÖ¤£º|PQ|=|PF2|£»
£¨2£©ÇóµãTµÄ¹ì¼£CµÄ·½³Ì£»
£¨3£©ÈôÍÖÔ²µÄÀëÐÄÂÊe=
| ||
2 |
£¨1£©ÓÉÍÖÔ²µÄ¶¨ÒåÓÐ|PF1|+|PF2|=2a£¬
ÓÖ|QF1|=|PF1|+|QP|=2a£¬
¡à|PQ|=|PF2|£®
£¨2£©ÓÉ£¨1£©µÃ|PQ|=|PF2|£¬ÓÖ
•
=0£¬|
|¡Ù0£®
¡àµãTΪQF2µÄÖе㣬
ÓÖµãOÊÇÏ߶ÎF1F2µÄÖе㣬
¡àOTÊÇ¡÷QF1F2µÄÖÐλÏߣ®
¡à|OT|=
|QF1|=a£¬ËùÒÔµãTµÄ¹ì¼£CµÄ·½³ÌÊÇx2+y2=a2£®
£¨3£©¼ÙÉèCÉÏ´æÔÚµãM£¨x0£¬y0£©Ê¹S=b2µÄ³äÒªÌõ¼þÊÇ
£¬
ÓÉÌâÒâµÃ|y0|¡Üa£¬ÓÉ£¨4£©µÃ|y0|=
£®
ËùÒÔÈôÒª´æÔÚµãM£¬Ê¹S=b2£¬±ØÐëa¡Ý
£¬¼´ac¡Ýb2 £¬
¡àac¡Ýa2-c2£¬Á½±ßͬ³ýÒÔa2µÃe2+e-1¡Ý0£¬½âµÃ
¡Üe£¼1£¬»òe¡Ü
£¨ÉáÈ¥£©£®
¡ß
¡Ê[
£¬1£©£¬
¹Êµ±ÍÖÔ²µÄÀëÐÄÂÊe=
ʱ£¬¹ì¼£CÉÏ´æÔÚµãM£¬Ê¹¡÷F1MF2µÄÃæ»ýS=b2£®
ÔÚ´ËÌõ¼þÏ£¬
=(-c-x0£¬-y0)£¬
=(c-x0£¬-y0)£¬
ÓÉ
•
=
-c2+
=a2-c2=b2£¬
•
=|
|•|
|cos¡ÏF1MF2£¬S=
|
|•|
|sin¡ÏF1MF2=b2£¬
µÃtan¡ÏF1MF2=2£®
ÓÖ|QF1|=|PF1|+|QP|=2a£¬
¡à|PQ|=|PF2|£®
£¨2£©ÓÉ£¨1£©µÃ|PQ|=|PF2|£¬ÓÖ
PT |
TF2 |
TF2 |
¡àµãTΪQF2µÄÖе㣬
ÓÖµãOÊÇÏ߶ÎF1F2µÄÖе㣬
¡àOTÊÇ¡÷QF1F2µÄÖÐλÏߣ®
¡à|OT|=
1 |
2 |
£¨3£©¼ÙÉèCÉÏ´æÔÚµãM£¨x0£¬y0£©Ê¹S=b2µÄ³äÒªÌõ¼þÊÇ
|
ÓÉÌâÒâµÃ|y0|¡Üa£¬ÓÉ£¨4£©µÃ|y0|=
b2 |
c |
ËùÒÔÈôÒª´æÔÚµãM£¬Ê¹S=b2£¬±ØÐëa¡Ý
b2 |
c |
¡àac¡Ýa2-c2£¬Á½±ßͬ³ýÒÔa2µÃe2+e-1¡Ý0£¬½âµÃ
| ||
2 |
-
| ||
2 |
¡ß
| ||
2 |
| ||
2 |
¹Êµ±ÍÖÔ²µÄÀëÐÄÂÊe=
| ||
2 |
ÔÚ´ËÌõ¼þÏ£¬
MF1 |
MF2 |
ÓÉ
MF1 |
MF2 |
x | 20 |
y | 20 |
MF1 |
MF2 |
MF1 |
MF2 |
1 |
2 |
MF1 |
MF2 |
µÃtan¡ÏF1MF2=2£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿