法线和切线方程公式有哪些？
法线和切线方程公式是y=f'(a)(x-a)+f(a)和α*β=-1。法线是指始终垂直于某平面的虚线。在数学几何中法线指平面上垂直于曲线在某点的切线的一条线。几何上，切线指的是一条刚好触碰到曲线上某一点的直线。在物理学中过入射点垂直于镜面的直线叫做法线。对于立体表面而言，法线是有方向的：一般来说，由立体的内部指向外部的是法线正方向，反过来的是法线负方向。另外切线的判定定理是：一直线若与一圆有交点，且连接交点与圆心的直线与该直线垂直，那么这条直线就是圆的切线。
绛旓細鍒囩嚎涓庢硶绾鐨勫叧绯鍏紡锛氬垏绾跨殑鏂滅巼涔樹互娉曠嚎鐨勬枩鐜囷紳-1銆傚嵆鏂滅巼k=tan胃锛屛稿炬枩瑙択1*k2=tan胃锛妕an(胃锛90掳)=tan胃锛(-cot胃锛=-1銆傜敤瀵兼暟琛ㄧず鏇茬嚎y=f(x)鍦ㄧ偣M锛坸0,y0锛夊鐨鍒囩嚎鏂圭▼涓猴細y-f(x0)=f'(x0)(x-x0)娉曠嚎鏂圭▼涓猴細y-f(x0)=(-1/f'(x0))*(x-x0)銆傛牴鎹柟绋嬫眰瑙...
绛旓細鍏充簬娉曠嚎鏂圭▼涓庡垏绾挎柟绋嬪叕寮锛屾硶绾挎柟绋嬭繖涓緢澶氫汉杩樹笉鐭ラ亾锛屼粖澶╂潵涓哄ぇ瀹惰В绛斾互涓婄殑闂锛岀幇鍦ㄨ鎴戜滑涓璧锋潵鐪嬬湅鍚э紒1銆佸浜庣洿绾裤2銆佹硶绾挎槸瀹冪殑鍨傜嚎锛屽浜庝竴鑸殑骞抽潰鏇茬嚎锛涙硶绾垮氨鏄垏绾跨殑鍨傜嚎锛涘浜庣┖闂村浘褰紝灏辫鍙樻垚娉曞钩闈簡銆3銆佹硶绾挎枩鐜囦笌鍒囩嚎鏂滅巼涔樼Н涓-1锛屽嵆鑻ユ硶绾挎枩鐜囧拰鍒囩嚎鏂滅巼鍒嗗埆鐢ㄎ便佄茶〃绀猴紝...
绛旓細鍒囩嚎鏂圭▼鍜屾硶绾挎柟绋嬫槸鍥犱负鏈夈婂叕鍏辩殑鍒囩偣銆嬫墍浠ュ彉閲忔槸閫氱殑銆傚垏绾挎柟绋嬪拰娉曠嚎鏂圭▼鐨勫叧绯绘槸鐩镐簰鍨傜洿锛屽叕鍏辩偣鏄垏鐐癸紝杩囧垏鐐涓庡垏绾鍨傜洿鐨勭洿绾夸负娉曠嚎銆傝鏇茬嚎涓簓=f(x)鍒欏湪鐐(a锛宖(a))澶勭殑鍒囩嚎鏂圭▼涓猴細y=f'(a)(x-a)+f(a)锛娉曠嚎鏂圭▼鍏紡锛毼*尾=-1銆傜敱鍩烘湰鍑芥暟鐨...銆
绛旓細6銆佺殑鍒囩嚎鏂圭▼涓 mxa^2+nyb^2=1 4杩囧弻鏇茬嚎 x^2a^2y^2b^2=1 涓婁竴鐐筆m锛宯鐨勫垏绾挎柟绋嬩负 mxa^2nyb^2=1 5杩囨姏鐗╃嚎 y^2=2px 涓婁竴鐐筆m锛宯鐨勫垏绾挎柟绋嬩负 ny=px+m銆7銆娉曠嚎鍜屽垏绾挎柟绋嬪叕寮鏄痽=f#39axa+fa鍜屛*尾=1娉曠嚎鏄寚濮嬬粓鍨傜洿浜庢煇骞抽潰鐨勮櫄绾垮湪鏁板鍑犱綍涓硶绾挎寚骞抽潰涓婂瀭鐩翠簬鏇茬嚎鍦ㄦ煇...
绛旓細鏂规硶1锛歬=tan伪=锛坹2-y1锛/锛坸2-x1锛夋垨锛坹1-y2锛/锛坸1-x2锛夋柟娉2锛氭硶绾挎枩鐜涓庡垏绾鏂滅巼涔樼Н涓-1锛屽嵆鑻ユ硶绾挎枩鐜鍜屽垏绾鏂滅巼鍒嗗埆鐢ㄎ便佄茶〃绀猴紝鍒欏繀鏈壩*尾=-1銆傛柟娉3锛氬凡鐭娉曠嚎鏂圭▼锛屽垯鍙戠幇鏂滅巼涓猴細ax+by+c=0涓紝k=锛峚/b.瀵逛簬鐩寸嚎锛屾硶绾挎槸瀹冪殑鍨傜嚎锛涘浜庝竴鑸殑骞抽潰鏇茬嚎锛屾硶绾垮氨鏄垏绾...
绛旓細1銆佷簩娆℃洸闈㈣繃鍦ㄧ偣澶勭殑鍒囧钩闈㈠強娉曠嚎鏂圭▼濡備笅锛歠(x锛寉锛寊) = x^2+2y^2+3z^2-36锛屽垯 fx ' = 2x = 2锛宖y ' = 4y = 8锛宖z ' = 6z = 18锛屽垏骞抽潰鏂圭▼涓 2(x-1)+8(y-2)+18(z-3) = 0锛屾硶绾挎柟绋嬩负 (x-1)/2 = (y-2)/8 = (z-3)/18 銆2銆佸垏骞抽潰鍙婃硶绾挎柟绋嬭绠...
绛旓細k = y ' = cos(鍏/3) = 1/2锛屽洜姝鍒囩嚎鏂圭▼涓 y - 鈭3/2 = 1/2*(x - 鍏/3) 锛娉曠嚎鏂圭▼涓 y - 鈭3/2 = -2*(x - 鍏/3) 銆
绛旓細2銆佹硶绾跨殑鏂滅巼绛変簬鍒囩嚎鏂滅巼鐨勭浉鍙嶆暟锛屽嵆濡傛灉鍒囩嚎鏂滅巼涓簁锛岄偅涔堟硶绾挎枩鐜囦负-1/k銆娉曠嚎涓庡垏绾鐨勬枩鐜囧叧绯鍏紡鏄細k=tan伪锛濓紙y2-y1锛夛紡锛坸2-x1锛夋垨锛坹1-y2锛夛紡锛坸1-x2锛夈傛硶绾挎枩鐜囦笌鍒囩嚎鏂滅巼涔樼Н涓猴紞1锛屽嵆鑻ユ硶绾挎枩鐜囧拰鍒囩嚎鏂滅巼鍒嗗埆鐢ㄎ便佄茶〃绀猴紝鍒欏繀鏈壩憋紛尾锛濓紞1銆傚凡鐭娉曠嚎鏂圭▼锛屽垯鍙戠幇鏂滅巼涓...
绛旓細鍒囩嚎鏂圭▼涓猴細娉曠嚎鏂圭▼涓猴細
绛旓細瀵兼暟鍏紡:f鈥欙紙x_0锛=lim{ [f(x锛- f锛坸_0)]/(x - x_0 ) },x鈫抶_0 鍒囩嚎鏂圭▼锛歽 - f锛坸_0锛 = f鈥欙紙x_0锛夛紙x - x_0 锛娉曠嚎鏂圭▼: y - f锛坸_0锛 = [-1/f鈥欙紙x_0锛塢锛坸 - x_0 锛変緥锛氾紙1锛墆 = x^3, p(2,8);f鈥欙紙2锛=lim(x^3-8)/(x - 2 )=...
