ÌâÄ¿ÄÚÈÝ
ÒÑ֪˫ÇúÏß
-
=1ÓëÍÖÔ²
+
=1£¨a£¾b£¾0£©ÓÐÏàͬµÄ½¹µã£¬µãA£¬B·Ö±ðÊÇÍÖÔ²×óÓÒ¶¥µã£¬ÈôÍÖÔ²¹ýµãD£¨
£¬
£©£®
£¨1£©ÇóÍÖÔ²·½³Ì£»
£¨2£©ÒÑÖªFÊÇÍÖÔ²µÄÓÒ½¹µã£¬ÒÔAFΪֱ¾¶µÄÔ²¼ÇΪԲC£¬¹ýDµãÒýÔ²CµÄÇÐÏߣ¬ÊÔÇóÇÐÏß·½³Ì£»
£¨3£©ÉèMΪÍÖÔ²ÓÒ×¼ÏßÉÏ×Ý×ø±ê²»Îª0µÄµã£¬N£¨x0£¬y0£©ÊÇÔ²CÉϵÄÈÎÒâÒ»µã£¬ÊÇ·ñ´æÔÚ¶¨µãP£¬Ê¹µÃMN/PNµÈÓÚ³£Êý2£¬Èô´æÔÚ£¬Çó³ö¶¨µãPµÄ×ø±ê£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®
x2 |
9 |
y2 |
7 |
x2 |
a2 |
y2 |
b2 |
3 |
2 |
5
| ||
2 |
£¨1£©ÇóÍÖÔ²·½³Ì£»
£¨2£©ÒÑÖªFÊÇÍÖÔ²µÄÓÒ½¹µã£¬ÒÔAFΪֱ¾¶µÄÔ²¼ÇΪԲC£¬¹ýDµãÒýÔ²CµÄÇÐÏߣ¬ÊÔÇóÇÐÏß·½³Ì£»
£¨3£©ÉèMΪÍÖÔ²ÓÒ×¼ÏßÉÏ×Ý×ø±ê²»Îª0µÄµã£¬N£¨x0£¬y0£©ÊÇÔ²CÉϵÄÈÎÒâÒ»µã£¬ÊÇ·ñ´æÔÚ¶¨µãP£¬Ê¹µÃMN/PNµÈÓÚ³£Êý2£¬Èô´æÔÚ£¬Çó³ö¶¨µãPµÄ×ø±ê£»Èô²»´æÔÚ£¬Çë˵Ã÷ÀíÓÉ£®
¿¼µã£ºÖ±ÏßÓëԲ׶ÇúÏßµÄ×ÛºÏÎÊÌâ
רÌ⣺¼ÆËãÌâ,Բ׶ÇúÏßÖеÄ×îÖµÓ뷶ΧÎÊÌâ
·ÖÎö£º£¨1£©ÓÉÌâÒâÒ×Öªc=4£¬¹Ê¿ÉµÃ
£¬´Ó¶ø½âÍÖÔ²µÄ·½³Ì£»
£¨2£©Ð´³öF£¨4£¬0£©£¬A£¨-6£¬0£©£¬Ô²CµÄ·½³ÌΪ£º£¨x+1£©2+y2=25£¬Ò×ÖªµãD £¨
£¬
£©ÔÚÔ²CÉÏ£¬´Ó¶øÇóÇÐÏß·½³Ì£»
£¨3£©ÍÖÔ²ÓÒ×¼Ïß·½³ÌΪx=
=9£¬¹ÊM£¨9£¬d£©£¬N£¨-1+5cos¦Á£¬5sin¦Á£©£¬P£¨m£¬n£©£»ÔòÓÉ
=2µÃ£¨10-5cos¦Á£©2+£¨5sin¦Á-d£©2=4[£¨-m-1+5cos¦Á£©2+£¨5sin¦Á-n£©2]£¬»¯¼ò¿ÉµÃ
£¬´Ó¶ø½â³öm£¬n£¬d£®
|
£¨2£©Ð´³öF£¨4£¬0£©£¬A£¨-6£¬0£©£¬Ô²CµÄ·½³ÌΪ£º£¨x+1£©2+y2=25£¬Ò×ÖªµãD £¨
3 |
2 |
5
| ||
2 |
£¨3£©ÍÖÔ²ÓÒ×¼Ïß·½³ÌΪx=
a2 |
c |
MN |
PN |
|
½â´ð£º
½â£º£¨1£©ÓÉÌâÒ⣬˫ÇúÏß
-
=1µÄ×óÓÒ½¹µãΪ£¨¡À4£¬0£©£¬
¹Êc=4£¬
Ôò¿ÉµÃ
£¬
½âµÃ£¬a2=36£¬b2=20£»
¹ÊÍÖÔ²·½³ÌΪ£º
+
=1£»
£¨2£©F£¨4£¬0£©£¬A£¨-6£¬0£©£¬
¹ÊÔ²CµÄ·½³ÌΪ£º£¨x+1£©2+y2=25£¬
Ò×ÖªµãD £¨
£¬
£©ÔÚÔ²CÉÏ£¬
kCD=
=
£¬
¹ÊÇÐÏßµÄбÂÊk=-
£¬
¹ÊÇÐÏß·½³ÌΪy-
=-
£¨x-
£©£¬
»¯¼òµÃ£¬x+
y-9=0£»
£¨3£©ÍÖÔ²ÓÒ×¼Ïß·½³ÌΪx=
=9£¬
¹ÊM£¨9£¬d£©£¬N£¨-1+5cos¦Á£¬5sin¦Á£©£¬P£¨m£¬n£©£»
ÔòÓÉ
=2µÃ£¬
£¨10-5cos¦Á£©2+£¨5sin¦Á-d£©2=4[£¨-m-1+5cos¦Á£©2+£¨5sin¦Á-n£©2]£¬
»¯¼ò¿ÉµÃ£¨40£¨m+1£©-100£©cos¦Á+£¨40n-10d£©sin¦Á+d2+25-4£¨m+1£©2-4n2=0£¬
Ôò
£¬
½âµÃ£¬m=
£¬n=d=0£»
ÕâÓëÌâÒâMΪÍÖÔ²ÓÒ×¼ÏßÉÏ×Ý×ø±ê²»Îª0µÄµãÏàì¶Ü£¬
¹Ê¼ÙÉè²»³ÉÁ¢£¬
¹Ê²»´æÔÚ£®
x2 |
9 |
y2 |
7 |
¹Êc=4£¬
Ôò¿ÉµÃ
|
½âµÃ£¬a2=36£¬b2=20£»
¹ÊÍÖÔ²·½³ÌΪ£º
x2 |
36 |
y2 |
20 |
£¨2£©F£¨4£¬0£©£¬A£¨-6£¬0£©£¬
¹ÊÔ²CµÄ·½³ÌΪ£º£¨x+1£©2+y2=25£¬
Ò×ÖªµãD £¨
3 |
2 |
5
| ||
2 |
kCD=
| ||||
|
3 |
¹ÊÇÐÏßµÄбÂÊk=-
| ||
3 |
¹ÊÇÐÏß·½³ÌΪy-
5
| ||
2 |
| ||
3 |
3 |
2 |
»¯¼òµÃ£¬x+
3 |
£¨3£©ÍÖÔ²ÓÒ×¼Ïß·½³ÌΪx=
a2 |
c |
¹ÊM£¨9£¬d£©£¬N£¨-1+5cos¦Á£¬5sin¦Á£©£¬P£¨m£¬n£©£»
ÔòÓÉ
MN |
PN |
£¨10-5cos¦Á£©2+£¨5sin¦Á-d£©2=4[£¨-m-1+5cos¦Á£©2+£¨5sin¦Á-n£©2]£¬
»¯¼ò¿ÉµÃ£¨40£¨m+1£©-100£©cos¦Á+£¨40n-10d£©sin¦Á+d2+25-4£¨m+1£©2-4n2=0£¬
Ôò
|
½âµÃ£¬m=
3 |
2 |
ÕâÓëÌâÒâMΪÍÖÔ²ÓÒ×¼ÏßÉÏ×Ý×ø±ê²»Îª0µÄµãÏàì¶Ü£¬
¹Ê¼ÙÉè²»³ÉÁ¢£¬
¹Ê²»´æÔÚ£®
µãÆÀ£º±¾Ì⿼²éÁËԲ׶ÇúÏߵĻ¯¼òÓëÓ¦Ó㬻¯¼òºÜÀ§ÄÑ£¬ÊôÓÚÄÑÌ⣮
Á·Ï°²áϵÁдð°¸
Ïà¹ØÌâÄ¿
ÒÑ֪ƽÃæÏòÁ¿
=£¨2m+1£¬3£©
=£¨2£¬m£©£¬ÇÒ
¡Î
£¬ÔòʵÊýmµÄÖµµÈÓÚ£¨¡¡¡¡£©
a |
b£¬ |
a |
b |
A¡¢2»ò-
| ||
B¡¢
| ||
C¡¢-2»ò
| ||
D¡¢-
|
ÒÑÖª
+
=1£¨m£¾0£¬n£¾0£©£¬Ôòµ±m+nÈ¡µÃ×îСֵʱ£¬ÍÖÔ²
+
=1µÄ·½³ÌΪ£¨¡¡¡¡£©
1 |
m |
2 |
n |
x2 |
m |
y2 |
n |
A¡¢
| ||||||||
B¡¢
| ||||||||
C¡¢
| ||||||||
D¡¢
|