鍦嗛敟鏇茬嚎棰樺瀷
涓庡渾閿ユ洸绾挎湁鍏崇殑鍑犵鍏稿瀷棰橈紝
濡傚渾閿ユ洸绾跨殑寮﹂暱姹傛硶銆?/p>
涓庡渾閿ユ洸绾挎湁鍏崇殑
鏈�鍊?/p>
(
鏋佸�?/p>
)
闂銆佷笌鍦嗛敟鏇茬嚎鏈夊叧鐨勮瘉鏄庨棶棰樹互鍙婂渾閿ユ洸绾夸笌鍦嗛敟鏇茬嚎鏈夊叧鐨勮瘉
鏄庨棶棰樼瓑锛屽湪鍦嗛敟鏇茬嚎鐨勭患鍚堝簲鐢ㄤ腑缁忓父瑙佸埌锛屼负浜嗚鍚屽浠杩欐柟闈㈢殑鐭ヨ瘑鏈?/p>
涓�涓瘮杈冪郴缁熺殑浜嗚В锛屾湰鏂囩郴缁熼槓杩颁竴涓嬧�滀笌鍦嗛敟鏇茬嚎鏈夊叧鐨勫嚑绉嶅吀鍨嬮鈥濓紟
涓�銆侀噸銆侀毦銆佺枒鐐瑰垎鏋?/p>
1
锛庨噸鐐癸細鍦嗛敟鏇茬嚎鐨勫鸡闀挎眰娉曘�佷笌鍦嗛敟鏇茬嚎鏈夊叧鐨勬渶鍊?/p>
(
鏋佸�?/p>
)
闂銆佷笌鍦?/p>
閿ユ洸绾挎湁鍏崇殑璇佹槑闂锛?/p>
2
锛庨毦鐐癸細鍙屽渾閿ユ洸绾跨殑鐩镐氦闂锛?/p>
(
搴斿綋鎻愰啋娉ㄦ剰鐨勬槸
:
闄や簡瑕佺敤涓�鍏冧簩娆?/p>
鏂圭▼鐨勫垽鍒紡锛岃繕瑕佺粨鍚堝浘褰㈠垎鏋愶紟
)
3
锛庣枒鐐癸細涓庡渾閿ユ洸绾挎湁鍏崇殑璇佹槑闂锛?/p>
(
瑙ｅ喅鍔炴硶锛氬洜涓鸿繖绫婚棶棰樻秹鍙婂埌绾?/p>
娈电浉绛夈�佽鐩哥瓑銆佺洿绾垮钩琛屻�佸瀭鐩寸殑璇佹槑鏂规硶锛屼互鍙婂畾鐐广�佸畾鍊奸棶棰樼殑鍒ゆ柇鏂规硶锛?/p>
鎵�浠ユ瘮杈冪伒娲伙紝鍙兘閫氳繃涓�浜涗緥棰樹簣浠ョず鑼冿紟
)
浜屻�侀鍨嬪睍绀?/p>
1
锛庡渾閿ユ洸绾跨殑寮﹂暱姹傛硶
璁惧渾閿ユ洸绾?/p>
C
鈭?/p>
f(x
锛?/p>
y)=0
涓庣洿绾?/p>
l
鈭?/p>
y=kx+b
鐩镐氦浜?/p>
A(
1
1
,
y
x
)
銆?/p>
B(
2
2
,
y
x
)
涓ょ偣锛屽垯寮﹂暱
|AB|
涓猴細
(2)
鑻ュ鸡
AB
杩囧渾閿ユ洸绾跨殑鐒︾偣
F
锛屽垯鍙敤鐒﹀崐寰勬眰寮﹂暱锛?/p>
|AB|=|AF|+|BF|
锛?/p>
渚?/p>
1
杩囨姏鐗╃嚎
2
4
1
x
y
飥?
飥?/p>
鐨勭劍鐐逛綔鍊炬枩瑙掍负
飦?/p>
鐨勭洿绾?/p>
l
涓庢姏鐗╃嚎浜や簬
A
銆?/p>
B
涓?/p>
鐐癸紝鏃?/p>
|AB|=8
锛屾眰鍊炬枩瑙?/p>
飦?/p>
锛?/p>
鍒嗘瀽涓�锛氱敱寮﹂暱鍏紡鏄撹В锛庤В绛斾负锛?/p>
鈭?/p>
鎶涚墿绾挎柟绋嬩负
x2=-4y
锛?/p>
鈭寸劍鐐逛负
(0
锛?/p>
-1)
锛?/p>
璁剧洿绾?/p>
l
鐨勬柟绋嬩负
y-(-1)=k(x-0)
锛屽嵆
y=kx-1
锛?/p>
灏嗘寮忎唬鍏?/p>
x2=-4y
涓緱锛?/p>
x2+4kx-4=0
锛庘埓x1+x
2
=-4
锛?/p>
x1+x2=-4k
锛?/p>
鐢?/p>
|AB|=8
寰?/p>
:
飥?/p>
飥?/p>
飥?/p>
飥?/p>
4
1
4
4
1
8
2
2
飥?/p>
飩?/p>
飩?/p>
飥?/p>
飥?/p>
飪?/p>
飥?/p>
飥?/p>
k
k
鈭?/p>
1
飩?/p>
飥?/p>
k
鍙堟湁
1
tan
飩?/p>
飥?/p>
飦?/p>
寰?/p>
:
4
飦?
飦?/p>
飥?
鎴?/p>
4
3
飦?/p>
飦?/p>
飥?
.
鍒嗘瀽浜?/p>
:
鍒╃敤鐒﹀崐寰勫叧绯?/p>
鈭?/p>
2
,
2
2
1
p
y
BF
p
y
AF
飥?/p>
飥?/p>
飥?/p>
飥?
飥?/p>
飥?/p>
鈭磡AB|=
-(
1
y
+y
2
)+p=-[(kx
1
-1)+(kx
2
-1)]+p=-k(
1
x
+x
2
)+2+p
锛庣敱涓婅堪瑙ｆ硶
鏄撴眰寰楃粨鏋滐紝鍙敱鍚屽浠嚜宸辫瘯璇曞畬鎴愶紟
2
锛庝笌鍦嗛敟鏇茬嚎鏈夊叧鐨勬渶鍊?/p>
(
鏋佸�?/p>
)
鐨勯棶棰?/p>
鍦ㄨВ鏋愬嚑浣曚腑姹傛渶鍊硷紝
鍏抽敭鏄缓绔嬫墍姹傞噺鍏充簬鑷彉閲忕殑鍑芥暟鍏崇郴锛?/p>
鍐嶅埄鐢ㄤ唬
鏁版柟娉曟眰鍑虹浉搴旂殑鏈�鍊硷紟娉ㄦ剰鐐规槸瑕佽�冭檻鏇茬嚎涓婄偣鍧愭爣
(x
锛?/p>
y)
鐨勫彇鍊艰寖鍥达紟
渚?/p>
2
宸茬煡
2
x
+4(y-1)
2
=4
锛屾眰锛?/p>
(1)
2
x
+y
2
鐨勬渶澶у�间笌鏈�灏忓�?/p>
;(2)x+y
鐨勬渶澶?
鍊间笌鏈�灏忓�硷紟
瑙ｄ竴锛氬皢
2
x
+4(y-1)
2
=4
浠ｅ叆寰楋細
2
x
+y
2
=4-4(y-1)2+y
2
=-3y
2
+8y
鐢辩偣
(x
锛?/p>
y)
婊¤冻
2
x
+4(y-1)2=4
鐭ワ細
4(y-1)
2
鈮?/p>
4
鍗?/p>
|y-1|
鈮?/p>
1
锛庘埓
0
鈮?/p>
y
鈮?/p>
2
锛?/p>
褰?/p>
y=0
鏃讹紝
(
2
x
+y
2
)min=0
锛?/p>
瑙ｄ簩锛氬垎鏋愶細鏄剧劧閲囩敤
(1)
涓柟娉曡涓嶉�氾紟濡傛灉浠?/p>
u=x+y
锛屽垯灏嗘浠ｅ叆
2
x
+4(y-1)
2
=4
涓緱鍏充簬
y
鐨勪竴鍏冧簩娆℃柟绋嬶紝鍊熷姪浜庡垽鍒紡鍙眰寰楁渶鍊硷紟
浠?/p>
x+y=u
锛?/p>
鍒欐湁
x=u-y,
浠ｅ叆
2
x
+4(y-1)2=4
寰楋細
5
2
y
-(2u+8)y+
2
u
=0
锛?/p>