楂樹腑鏁板绔炶禌涓撻璁插骇锛堣В鏋愬嚑浣曪級
涓�銆佸熀纭�鐭ヨ瘑
1
锛庢き鍦嗙殑瀹氫箟锛岀涓�瀹氫箟锛氬钩闈笂鍒颁袱涓畾鐐圭殑璺濈涔嬪拰绛変簬瀹氶暱锛堝ぇ浜庝袱涓畾鐐逛箣闂寸殑
璺濈锛夌殑鐐圭殑杞ㄨ抗锛屽嵆
|PF
1
|+|PF
2
|=2a (2a>|F
1
F
2
|=2c).
绗簩瀹氫箟锛?/p>
骞抽潰涓婂埌涓�涓畾鐐圭殑璺濈涓庡埌涓�鏉″畾鐩寸嚎鐨勮窛绂讳箣姣斾负鍚屼竴涓父鏁?/p>
e(0<e<1)
鐨勭偣
鐨勮建杩癸紙鍏朵腑瀹氱偣涓嶅湪瀹氱洿绾夸笂锛?/p>
锛屽嵆
e
d
PF
飥?/p>
|
|
(0<e<1).
绗笁瀹氫箟锛氬湪鐩磋鍧愭爣骞抽潰鍐呯粰瀹氫袱鍦?/p>
c
1
: x
2
+y
2
=a
2
, c
2
: x
2
+y
2
=b
2
, a, b
鈭?/p>
R
+
涓?/p>
a
鈮?/p>
b
銆備粠鍘熺偣鍑?/p>
鍙戠殑灏勭嚎浜ゅ渾
c
1
浜?/p>
P
锛屼氦鍦?/p>
c
2
浜?/p>
Q
锛岃繃
P
寮?/p>
y
杞寸殑骞宠绾匡紝杩?/p>
Q
寮?/p>
x
杞寸殑骞宠绾匡紝涓ゆ潯绾?/p>
鐨勪氦鐐圭殑杞ㄨ抗鍗充负妞渾銆?/p>
2
锛庢き鍦嗙殑鏂圭▼锛屽鏋滀互妞渾鐨勪腑蹇冧负鍘熺偣锛岀劍鐐规墍鍦ㄧ殑鐩寸嚎涓哄潗鏍囪酱寤虹珛鍧愭爣绯伙紝鐢卞畾涔?/p>
鍙眰寰楀畠鐨勬爣鍑嗘柟绋嬶紝鑻ョ劍鐐瑰湪
x
杞翠笂锛屽垪鏍囧噯鏂圭▼涓?/p>
1
2
2
2
2
飥?/p>
飥?/p>
b
y
a
x
(a>b>0)
锛?/p>
鍙傛暟鏂圭▼涓?/p>
飪?
飪?
飪?/p>
飥?/p>
飥?/p>
飦?/p>
飦?
sin
cos
b
y
a
x
锛?/p>
飦?/p>
涓哄弬鏁帮級
銆?/p>
鑻ョ劍鐐瑰湪
y
杞翠笂锛屽垪鏍囧噯鏂圭▼涓?/p>
1
2
2
2
2
飥?/p>
飥?/p>
b
y
a
y
(a>b>0)
銆?/p>
3
锛庢き鍦嗕腑鐨勭浉鍏虫蹇碉紝瀵逛簬涓績鍦ㄥ師鐐癸紝鐒︾偣鍦?/p>
x
杞翠笂鐨勬き鍦?/p>
1
2
2
2
2
飥?/p>
飥?/p>
b
y
a
x
锛?/p>
a
绉板崐闀胯酱闀匡紝
b
绉板崐鐭酱闀匡紝
c
绉颁负鍗婄劍璺濓紝闀胯酱绔偣銆佺煭杞寸鐐广�佷袱涓劍鐐圭殑鍧愭爣鍒嗗埆
涓?/p>
(
卤
a,
0
), (0,
卤
b
), (
卤
c,
0
)
锛涗笌宸︾劍鐐瑰搴旂殑鍑嗙嚎锛堝嵆绗簩瀹氫箟涓殑瀹氱洿绾匡級涓?/p>
c
a
x
2
飥?/p>
飥?/p>
锛?
涓庡彸鐒︾偣瀵瑰簲鐨勫噯绾夸负
c
a
x
2
飥?/p>
锛?/p>
瀹氫箟涓殑姣?/p>
e
绉颁负绂诲績鐜囷紝
涓?/p>
a
c
e
飥?/p>
锛?/p>
鐢?/p>
c
2
+b
2
=a
2
鐭?/p>
0<e<1.
妞渾鏈変袱鏉″绉拌酱锛屽垎鍒槸闀胯酱銆佺煭杞淬�?/p>
4
锛?/p>
妞渾鐨勭劍鍗婂緞鍏紡锛氬浜庢き鍦?/p>
飥?/p>
飥?/p>
2
2
2
2
b
y
a
x
1(a>b>0), F
1
(-c, 0), F
2
(c, 0)
鏄畠鐨勪袱鐒︾偣銆傝嫢
P(x,
y)
鏄き鍦嗕笂鐨勪换鎰忎竴鐐癸紝鍒?/p>
|PF
1
|=a+ex, |PF
2
|=a-ex.
5
锛庡嚑涓父鐢ㄧ粨璁猴細
1
锛夎繃妞渾涓婁竴鐐?/p>
P(x
0
, y
0
)
鐨勫垏绾挎柟绋嬩负
1
2
0
2
0
飥?/p>
飥?/p>
b
y
y
a
x
x
锛?/p>