圆锥曲线的弦长公式推导 直线截椭圆的弦长公式，要详细证明，一步步推导~谢谢~！
\u6c42\u89e3\u5706\u9525\u66f2\u7ebf\u7684\u5f26\u957f\u516c\u5f0f\u7684\u63a8\u5bfc\u8fc7\u7a0by=kx+b
\u5f26\u957fd=\u221a[(x1-x2)^2+(y1-y2)^2]
=\u221a[(x1-x2)^2+k^2(x1-x2)^2]
=\u221a\uff081+k^2\uff09\u221a[(x1-x2)^2]
=\u221a\uff081+k^2\uff09\u221a[(x1+x2)^2-
4x1x2]
\u5982\u679c\u7528y\u6765\u8868\u793a
x=1/k(y-b)
\u5c31\u4f1a\u5f97\u5230d
=
\u221a\uff081+k^2\uff09[(x1+x2\uff09^2
-
4x1x2]
=
\u221a\uff081+1/k^2\uff09[(y1+y2\uff09^2
-
4y1y2]
弦长d=√[(x1-x2)^2+(y1-y2)^2]
=√[(x1-x2)^2+k^2(x1-x2)^2]
=√（1+k^2）√[(x1-x2)^2]
=√（1+k^2）√[(x1+x2)^2- 4x1x2]
如果用y来表示
x=1/k(y-b)
就会得到d = √（1+k^2）[(x1+x2）^2 - 4x1x2] = √（1+1/k^2）[(y1+y2）^2 - 4y1y2]
绛旓細鍦嗛敟鏇茬嚎寮﹂暱鍏紡鏄鸡闀=|x1-x2|鈭氾紙k²+1锛銆傚渾閿ユ槸涓绉嶅嚑浣曞浘褰紝鏈変袱绉嶅畾涔夈傝В鏋愬嚑浣曞畾涔夛細鍦嗛敟闈㈠拰涓涓埅瀹冪殑骞抽潰(婊¤冻浜ょ嚎涓哄渾)缁勬垚鐨勭┖闂村嚑浣曞浘褰㈠彨鍦嗛敟銆傜珛浣撳嚑浣曞畾涔夛細浠ョ洿瑙掍笁瑙掑舰鐨勭洿瑙掕竟鎵鍦ㄧ洿绾夸负鏃嬭浆杞达紝鍏朵綑涓よ竟鏃嬭浆360搴﹁屾垚鐨勬洸闈㈡墍鍥存垚鐨勫嚑浣曚綋鍙仛鍦嗛敟銆傚渾閿ョ殑楂橈細鍦嗛敟鐨勯《...
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绛旓細鍏紡涓 d = 鈭(1+k²)|x1-x2| = 鈭(1+k²)[(x1+x2)² - 4x1x2] = 鈭(1+1/k²)|y1-y2| = 鈭(1+1/k²)[(y1+y2)² - 4y1y2]鍏充簬鐩寸嚎涓鍦嗛敟鏇茬嚎鐩镐氦姹寮﹂暱锛岄氱敤鏂规硶鏄皢鐩寸嚎y=kx+b浠ｅ叆鏇茬嚎鏂圭▼锛屽寲涓哄叧浜巟(鎴栧叧浜巠)鐨勪竴鍏冧簩娆℃柟绋嬶紝...
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