ÌâÄ¿ÄÚÈÝ

ÒÑ֪˫ÇúÏß
x2
9
-
y2
7
=1ÓëÍÖÔ²
x2
a2
+
y2
b2
=1£¨a£¾b£¾0£©ÓÐÏàͬµÄ½¹µã£¬µãA£¬B·Ö±ðÊÇÍÖÔ²×óÓÒ¶¥µã£¬ÈôÍÖÔ²¹ýµãD£¨
3
2
£¬
5
3
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
a2=b2+c2
c=4
9
4a2
+
75
4b2
=1
£¬´Ó¶ø½âÍÖÔ²µÄ·½³Ì£»
£¨2£©Ð´³öF£¨4£¬0£©£¬A£¨-6£¬0£©£¬Ô²CµÄ·½³ÌΪ£º£¨x+1£©2+y2=25£¬Ò×ÖªµãD £¨
3
2
£¬
5
3
2
£©ÔÚÔ²CÉÏ£¬´Ó¶øÇóÇÐÏß·½³Ì£»
£¨3£©ÍÖÔ²ÓÒ×¼Ïß·½³ÌΪx=
a2
c
=9£¬¹ÊM£¨9£¬d£©£¬N£¨-1+5cos¦Á£¬5sin¦Á£©£¬P£¨m£¬n£©£»ÔòÓÉ
MN
PN
=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=0
40n-10d=0
d2+25-4(m+1)2-4n2=0
£¬´Ó¶ø½â³öm£¬n£¬d£®
½â´ð£º ½â£º£¨1£©ÓÉÌâÒ⣬˫ÇúÏß
x2
9
-
y2
7
=1µÄ×óÓÒ½¹µãΪ£¨¡À4£¬0£©£¬
¹Êc=4£¬
Ôò¿ÉµÃ
a2=b2+c2
c=4
9
4a2
+
75
4b2
=1
£¬
½âµÃ£¬a2=36£¬b2=20£»
¹ÊÍÖÔ²·½³ÌΪ£º
x2
36
+
y2
20
=1£»
£¨2£©F£¨4£¬0£©£¬A£¨-6£¬0£©£¬
¹ÊÔ²CµÄ·½³ÌΪ£º£¨x+1£©2+y2=25£¬
Ò×ÖªµãD £¨
3
2
£¬
5
3
2
£©ÔÚÔ²CÉÏ£¬
kCD=
5
2
3
3
2
+1
=
3
£¬
¹ÊÇÐÏßµÄбÂÊk=-
3
3
£¬
¹ÊÇÐÏß·½³ÌΪy-
5
3
2
=-
3
3
£¨x-
3
2
£©£¬
»¯¼òµÃ£¬x+
3
y-9=0£»
£¨3£©ÍÖÔ²ÓÒ×¼Ïß·½³ÌΪx=
a2
c
=9£¬
¹ÊM£¨9£¬d£©£¬N£¨-1+5cos¦Á£¬5sin¦Á£©£¬P£¨m£¬n£©£»
ÔòÓÉ
MN
PN
=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
40(m+1)-100=0
40n-10d=0
d2+25-4(m+1)2-4n2=0
£¬
½âµÃ£¬m=
3
2
£¬n=d=0£»
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¿

Î¥·¨ºÍ²»Á¼ÐÅÏ¢¾Ù±¨µç»°£º027-86699610 ¾Ù±¨ÓÊÏ䣺58377363@163.com

¾«Ó¢¼Ò½ÌÍø