圆锥曲线的弦长公式 求解圆锥曲线的弦长公式的推导过程
\u5706\u9525\u66f2\u7ebf\u4e2d\u7684\u51e0\u79cd\u5f26\u957f\u516c\u5f0f\u662f\u4ec0\u4e48? r=ep/(1-ecosθ）绛旓細鍦嗛敟鏇茬嚎寮﹂暱鍏紡锛y=kx+b銆
绛旓細鏈変笁涓鸡闀垮叕寮忥細1銆佸崐寰勪负R銆佸渾蹇冭涓篴鏃讹細寮﹂暱=2Rsina锛2銆佸姬闀夸负L銆佸崐寰勪负R鏃讹細寮﹂暱=2Rsin(L*180/蟺R)锛3銆佺洿绾夸笌鍦嗛敟鏇茬嚎鐩镐氦鎵寰楀鸡闀挎椂锛寮﹂暱=鈹倄1-x2鈹傗垰(k^2+1)=鈹倅1-y2鈹傗垰[(1/k^2)+1]PS锛氬渾閿ユ洸绾匡紝 鏄暟瀛︺佸嚑浣曞涓氳繃骞冲垏鍦嗛敟锛堜弗鏍间负涓涓鍦嗛敟闈㈠拰涓涓钩闈㈠畬鏁...
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《...
绛旓細鍦嗛敟鏇茬嚎寮﹂暱鍏紡锛歞=鈭(1+k2)|x1-x2|銆傚濂藉渾閿ユ洸绾跨殑娉ㄦ剰浜嬮」锛1.鐗㈣鏍稿績鐭ヨ瘑鐐 妞渾锛屽弻鏇茬嚎绂诲績鐜囧叕寮忓拰鑼冨洿璁颁笉娓咃紝鐒︾偣鍒嗗埆鍦▁杞达紝y杞翠笂鐨勫弻鏇茬嚎鐨勬笎杩戠嚎鏂圭▼涔熷偦鍌诲垎涓嶆竻锛屽湪鍋氶鏃惰嚜鐒跺仛涓嶅銆2.璁＄畻鑳藉姏涓庨熷害 璁＄畻鑳藉姏寮虹殑鍚屽鍦ㄥ鍦嗛敟鏇茬嚎鏃剁浉瀵硅交鏉俱傚彲浠ュ皾璇曡缁冭嚜宸卞彛绠楀緱鍒拌仈绔嬪悗...
绛旓細寮﹂暱鍏紡锛屽湪杩欓噷鎸囩洿绾夸笌鍦嗛敟鏇茬嚎鐩镐氦鎵寰楀鸡闀縟鐨勫叕寮忋傚叕寮忎竴 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]鍏充簬鐩寸嚎涓庡渾閿ユ洸绾跨浉浜ゆ眰寮﹂暱锛岄氱敤鏂规硶鏄皢鐩寸嚎y=kx...
绛旓細鍦嗚鐩寸嚎鎴殑寮﹂暱鍏紡鏄鸡闀=鈹倄1-x2鈹傗垰(k^2+1)=鈹倅1-y2鈹傗垰[(1/k^2)+1]锛屽叾涓璳涓虹洿绾挎枩鐜囷紝(x1锛寉1)锛(x2锛寉2)涓虹洿绾夸笌鏇茬嚎鐨勪袱浜ょ偣锛屸攤鈹備负缁濆鍊肩鍙凤紝鈭氫负鏍瑰彿銆傚鸡闀夸负杩炴帴鍦嗕笂浠绘剰涓ょ偣鐨勭嚎娈电殑闀垮害銆傚鸡闀垮叕寮忥紝鍦ㄨ繖閲屾寚鐩寸嚎涓庡渾閿ユ洸绾跨浉浜ゆ墍寰楀鸡闀跨殑鍏紡銆傚渾閿ユ洸绾匡紝鏄暟瀛︺...
绛旓細1.妞渾鐨勫鸡闀垮叕寮 妞渾鏄渾閿ユ洸绾夸腑鐨勪竴绉嶏紝瀹冪殑寮﹂暱鍏紡濡備笅锛寮﹂暱=鈹倄1-x2鈹傗垰(k^2+1)=鈹倅1-y2鈹傗垰[(1/k^2)+1]2.鍙屾洸绾跨殑寮﹂暱鍏紡 鍙屾洸绾挎槸鍦嗛敟鏇茬嚎涓殑涓绉嶏紝瀹冪殑寮﹂暱鍏紡濡備笅锛歀 = |AB|=鈭 (1+k²) [ (X1+X2)²-4X1X2]3.鎶涚墿绾跨殑寮﹂暱鍏紡 鎶涚墿绾挎槸鍦嗛敟鏇茬嚎...
绛旓細鍏紡2绗﹀悎妞渾绛鍦嗛敟鏇茬嚎 涓嶅厜鏄渾銆傚叕寮/|a|鏄湪鏁翠釜 杩愮畻鍚庡啀杩涜鐨勨︹︼紙骞虫柟浜嗗啀闄わ級2寮忓彲浠ョ敱1鎺ㄥ嚭锛屽緢绠鍗曪紝鐢 锛寈1+x2=-b/a x1x2=c/a 甯﹀叆鍐 鍗冲彲鈥︹﹀湪鐭ラ亾鍦嗗拰 姹寮﹂暱鏃朵篃鍙互鐢 锛堢偣鍒扮洿绾胯窛绂汇佸崐寰勩佸崐寮︼級銆傚鏋滃府鍒版偍鐨勮瘽锛屽彲浠ュソ璇勫悧锛熻阿璋簡锛侊紒锛(鍙充笂瑙掗噰绾)...
绛旓細寮﹂暱鍏紡锛屾寚鐩寸嚎涓庡渾閿ユ洸绾跨浉浜ゆ墍寰楀鸡闀縟鐨勫叕寮忋寮﹂暱=鈹倄1-x2鈹傗垰(k^2+1)=鈹倅1-y2鈹傗垰[(1/k^2)+1] 銆傚叾涓璳涓虹洿绾挎枩鐜,(x1,y1),(x2,y2)涓虹洿绾夸笌鏇茬嚎鐨勪袱浜ょ偣,"鈹傗攤"涓虹粷瀵瑰肩鍙,"鈭"涓烘牴鍙枫傝鏄滃鸡闀垮叕寮忊濓紝鍏跺疄鏄袱鐐归棿鐨勮窛绂诲叕寮忊斺旂敱浜庢枩鐜噆宸茬煡浜嗭紝鎵浠ュ氨鑳界敤鏂滅巼銆佹í...
绛旓細鐩寸嚎涓庢き鍦嗙浉浜鐨勫鸡闀垮叕寮鏄細寮﹂暱=鈹倅1-y2鈹傗垰銆愶紙1/k²锛+1銆戙傚渾鐨勫鸡闀挎槸鍦嗗績瑙掓墍瀵圭殑寮︿笌鍦嗗績杩炵嚎锛堝嵆鍦嗕笂鐨勭偣鍒板渾蹇冪殑璺濈锛夈傚鸡闀=2Rsina锛孯鏄崐寰勶紝a鏄渾蹇冭锛涘鸡闀夸负杩炴帴鍦嗕笂浠绘剰涓ょ偣鐨勭嚎娈电殑闀垮害銆傚鸡闀垮叕寮忥紝鍦ㄨ繖閲屾寚鐩寸嚎涓鍦嗛敟鏇茬嚎鐩镐氦鎵寰寮﹂暱鐨鍏紡銆傚渾閿ユ洸绾匡紝鏄暟瀛︺佸嚑浣曞...
