ÍÖÔ²C1£¬Å×ÎïÏßC2µÄ½¹µã¾ùÔÚxÖáÉÏ£¬´ÓÁ½ÌõÇúÏßÉϸ÷È¡Á½¸öµã£¬½«Æä×ø±ê»ìºÏ¼Ç¼ÓÚϱíÖУº
x
3
4
6
y -
3
3
-2
2
£¨1£©ÇóC1£¬C2µÄ±ê×¼·½³Ì£®
£¨2£©Èçͼ£¬¹ýµãM£¨2£¬0£©µÄÖ±ÏßlÓëC2ÏཻÓÚA£¬BÁ½µã£¬AÔÚxÖáÏ·½£¬BÔÚxÖáÉÏ·½£¬ÇÒ
AM
=
1
2
MB
£¬ÇóÖ±ÏßlµÄ·½³Ì£»
£¨3£©Ó루2£©ÖÐÖ±ÏßlƽÐеÄÖ±Ïßl1ÓëÍÖÔ²½»ÓÚC£¬DÁ½µã£¬ÒÔCDΪµ×±ß×÷µÈÑü¡÷PCD£¬ÒÑÖªPµã×ø±êΪ£¨-3£¬2£©£¬Çó¡÷PCDµÄÃæ»ý£®
·ÖÎö£º£¨1£©ÉèÅ×ÎïÏß·½³ÌΪy2=mx£¬·Ö±ð½«Ëĸöµã´úÈëµÃµ½ÏàͬµÄmÖµÁ½¸öµã¼´¿É£¬½ø¶ø½«ÁíÍâÁ½¸öµãµÄ×ø±ê´úÈëÍÖÔ²·½³Ì¼´¿ÉµÃ³ö£»
£¨2£©ÉèÖ±ÏßlµÄ·½³ÌΪ£ºx=my+2£¬ÓëÅ×ÎïÏß·½³ÌÁªÁ¢ÏûÈ¥xµÃ£ºy2-my-2=0£¬ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬ÀûÓøùÓëϵÊýµÄ¹Øϵ¼°ÏòÁ¿ÏàµÈ
AM
=
1
2
MB
£¬¼´¿ÉµÃµ½mµÄÖµ£®£®
£¨3£©ÉèÖ±Ïßl1µÄ·½³ÌΪ£ºy=x+t£¬ÓëÍÖÔ²½»ÓÚC£¨x3£¬y3£©¡¢D£¨x4£¬y4£©Á½µã£¬ÖеãΪQ£¨x0£¬y0£©£¬ÔòPQΪl1µÄ´¹Ö±Æ½·ÖÏߣ¬ÀûÓá°µã²î·¨¡±¼´¿ÉµÃ£ºx0=-3y0£¬ÓÖy0=-x0-1£¬ÁªÁ¢½âµÃ£ºx0£¬y0£¬´úÈël1µÄ·½³Ì¿ÉµÃt£®¿ÉµÃl1µÄ·½³Ì£¬ÀûÓõãбʽ¼´¿ÉµÃ³öPQµÄ·½³ÌÓëÍÖÔ²·½³ÌÁªÁ¢¼´¿ÉµÃµ½C¡¢D×ø±ê£¬ÀûÓÃÁ½µã¼äµÄ¾àÀ빫ʽ¼´¿É|CD|=3
2
£¬ÀûÓõ㵽ֱÏߵľàÀ빫ʽ¿ÉµÃ£ºµãPµ½Ö±ÏßCD£¨l1£©µÄ¾àÀëh£¬ÀûÓÃS¡÷PCD=
1
2
|CD| ¡Áh
¼´¿É£®
½â´ð£º½â£º£¨1£©ÉèÅ×ÎïÏß·½³ÌΪy2=mx£¬·Ö±ð½«Ëĸöµã´úÈë½âµÃm=1£¬m=-
3
£¬m=1£¬m=
6
3
£¬
¹ÊÅ×ÎïÏß·½³ÌΪy2=x£»
Òò´Ë(
3
£¬
3
)
(
6
£¬-
2
)
Á½¸öµãΪÍÖÔ²C1ÉÏÁ½µã£¬
ÉèÍÖÔ²·½³ÌΪ£º
x2
a2
+
y2
b2
=1
£¬½«ÉÏÊöÁ½¸öµã×ø±ê´úÈë½âµÃ£ºa2=12£¬b2=4£¬
¹ÊÍÖÔ²·½³ÌΪ
x2
12
+
y2
4
=1
£®
£¨2£©ÉèÖ±ÏßlµÄ·½³ÌΪ£ºx=my+2£¬ÓëÅ×ÎïÏß·½³ÌÁªÁ¢£º
x=my+2
y2=x

ÏûÈ¥xµÃ£ºy2-my-2=0£¬
ÉèA£¨x1£¬y1£©£¬B£¨x2£¬y2£©£¬Ôò
y1+y2=m
y1y2=-2
£¬
ÓÖ
AM
=
1
2
MB
£¬
¡à-y1=
1
2
y2
£¬ÏûÈ¥y1£¬y2£¬
½âµÃ£ºm=1£¬
ËùÒÔÖ±ÏßlµÄ·½³ÌΪ£ºx=y+2£¬¼´x-y-2=0£®
£¨3£©ÉèÖ±Ïßl1µÄ·½³ÌΪ£ºy=x+t£¬ÓëÍÖÔ²½»ÓÚC£¨x3£¬y3£©¡¢D£¨x4£¬y4£©Á½µã£¬ÖеãΪQ£¨x0£¬y0£©£¬
ÔòPQΪl1µÄ´¹Ö±Æ½·ÖÏߣ¬
C¡¢DÔÚÍÖÔ²ÉϿɵãº
x
2
3
+3
y
2
3
=12
x
2
4
+3
y
2
4
=12
»¯Îª£¨x3+x4£©£¨x3-x4£©+3£¨y3+y4£©£¨y3-y4£©=0£¬
°Ñx0=
x3+x4
2
£¬y0=
y3+y4
2
£¬1=
y3-y4
x3-x4
£®´úÈë¿ÉµÃ£ºx0=-3y0£¬ÓÖy0=-x0-1£¬
ÁªÁ¢½âµÃ£ºx0=-
3
2
£¬y0=
1
2
£¬´úÈël1µÄ·½³Ì£¬t=2£®
¡àl1µÄ·½³ÌΪ£ºy=x+2£¬
¡àPQµÄ·½³ÌΪy-
1
2
=-(x+
3
2
)
£¬»¯Îªy=-x-1£®
ÁªÁ¢
y=x+2
x2+3y2=12
£¬½âµÃ
x=0
y=2
£¬
x=-3
y=-1
£¬C¡¢D×ø±ê£¬
¡à|CD|=
(-3-0)2+(-1-2)2
=3
2
£¬µãPµ½Ö±ÏßCD£¨l1£©µÄ¾àÀëh=
3
2
£®
¡àS¡÷PCD=
1
2
|CD| ¡Áh
=
1
2
¡Á3
2
¡Á
3
2
=
9
2
£®
µãÆÀ£ºÊìÁ·ÕÆÎÕÍÖÔ²ÓëÅ×ÎïÏߵıê×¼·½³Ì¼°ÆäÐÔÖÊ¡¢Ö±ÏßÓëԲ׶ÇúÏßµÄÏཻÎÊÌâת»¯Îª·½³ÌÁªÁ¢µÃµ½¸ùÓëϵÊýµÄ¹Øϵ¡¢¡°µã²î·¨¡±¡¢Öеã×ø±ê¹«Ê½¡¢Ð±ÂʼÆË㹫ʽ¡¢Á½µã¼äµÄ¾àÀ빫ʽ¡¢µãµ½Ö±ÏߵľàÀ빫ʽ¡¢Èý½ÇÐεÄÃæ»ý¹«Ê½µÈÊǽâÌâµÄ¹Ø¼ü£®
Á·Ï°²áϵÁдð°¸
Ïà¹ØÏ°Ìâ

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÍÖÔ²C1£º
x2
a2
+
y2
b2
=1(a£¾b£¾0)
µÄÓÒ½¹µãF2ÓëÅ×ÎïÏßC2£ºy2=4xµÄ½¹µãÖغϣ¬ÍÖÔ²C1ÓëÅ×ÎïÏßC2ÔÚµÚÒ»ÏóÏ޵Ľ»µãΪP£¬|PF2|=
5
3
£®Ô²C3µÄÔ²ÐÄTÊÇÅ×ÎïÏßC2ÉϵĶ¯µã£¬Ô²C3ÓëyÖá½»ÓÚM£¬NÁ½µã£¬ÇÒ|MN|=4£®
£¨1£©ÇóÍÖÔ²C1µÄ·½³Ì£»
£¨2£©Ö¤Ã÷£ºÎÞÂÛµãTÔ˶¯µ½ºÎ´¦£¬Ô²C3ºã¾­¹ýÍÖÔ²C1ÉÏÒ»¶¨µã£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÍÖÔ²C1£º
x2
a2
+
y2
b2
=1£¨a£¾b£¾0£©µÄ¶ÌÖ᳤Ϊ2£¬ÀëÐÄÂÊΪ
2
2
£»Å×ÎïÏßC2£ºy2=2px£¨p£¾0£©ÉÏÒ»µã£¨1£¬m £©µ½Æä½¹µãµÄ¾àÀëΪ2£®
£¨1£©ÇóÍÖÔ²C1ºÍÅ×ÎïÏßC2µÄ·½³Ì£»
£¨2£©ÉèÖ±ÏßlͬʱÓëÍÖÔ²C1ºÍÅ×ÎïÏßC2ÏàÇУ¬ÇóÖ±ÏßlµÄ·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

£¨2013•ºÓÎ÷Çøһģ£©ÒÑÖª¶Ô³ÆÖÐÐÄΪ×ø±êÔ­µãµÄÍÖÔ²C1ÓëÅ×ÎïÏßC2£ºx2=4yÓÐÒ»¸öÏàͬµÄ½¹µãF1£¬Ö±Ïßl£ºy=2x+mÓëÅ×ÎïÏßC2Ö»ÓÐÒ»¸ö¹«¹²µã£®
£¨1£©ÇóÖ±ÏßlµÄ·½³Ì£»
£¨2£©ÈôÍÖÔ²C1¾­¹ýÖ±ÏßlÉϵĵãP£¬µ±ÍÖÔ²C1µÄÀëÐÄÂÊÈ¡µÃ×î´óֵʱ£¬ÇóÍÖÔ²C1µÄ·½³Ì¼°µãPµÄ×ø±ê£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÀëÐÄÂÊΪ
1
2
µÄÍÖÔ²C1µÄ×ó¡¢ÓÒ½¹µã·Ö±ðΪF1£¬F2£¬Å×ÎïÏßC2£ºy2=4mx£¨m£¾0£©µÄ½¹µãΪF2£¬ÉèÍÖÔ²C1ÓëÅ×ÎïÏßC2µÄÒ»¸ö½»µãΪP£¨x'£¬y'£©£¬|PF1|=
7
3
£¬ÔòÍÖÔ²C1µÄ±ê×¼·½³ÌΪ
x2
4
+
y2
3
=1
x2
4
+
y2
3
=1
£»Å×ÎïÏßC2µÄ±ê×¼·½³ÌΪ
y2=4x
y2=4x
£®

²é¿´´ð°¸ºÍ½âÎö>>

¿ÆÄ¿£º¸ßÖÐÊýѧ À´Ô´£º ÌâÐÍ£º

ÒÑÖªÍÖÔ²C1£¬Å×ÎïÏßC2µÄ½¹µã¾ùÔÚyÖáÉÏ£¬C1µÄÖÐÐĺÍC2 µÄ¶¥µã¾ùΪ×ø±êÔ­µãO£¬´ÓÿÌõÇúÏßÉÏÈ¡Á½¸öµã£¬½«Æä×ø±ê¼Ç¼ÓÚϱíÖУº
x 0 -1
2
4
y -2
2
1
16
-2 1
£¨¢ñ£©Çó·Ö±ðÊʺÏC1£¬C2µÄ·½³ÌµÄµãµÄ×ø±ê£»
£¨¢ò£©ÇóC1£¬C2µÄ±ê×¼·½³Ì£®

²é¿´´ð°¸ºÍ½âÎö>>

ͬ²½Á·Ï°²á´ð°¸