高数。求切平面方程。请问这个1怎么处理？ 高数题。空间曲面的切平面方程 。怎么算都是1
\u9ad8\u6570\u7ebf\u6027\u4ee3\u6570\u3002\u5207\u5e73\u9762\u65b9\u7a0b\u3002\u8bf7\u95ee\u8fd9\u4e2a1\u600e\u4e48\u5904\u7406\uff1f\u8bbe\u5207\u5e73\u9762\u65b9\u7a0b\u4e3ax+2y+z+D=0.\u5219\u5207\u5e73\u9762\u6cd5\u5411\u91cf=\uff081,2,1\uff09,\u7531\u4e8e\u6cd5\u5411\u91cf\u53ef\u6b63\u53ef\u8d1f\uff0c\u6240\u4ee5\u5207\u5e73\u9762\u6cd5\u5411\u91cf\u8fd8\u7b49\u4e8e\uff08-1\uff0c-2\uff0c-1\uff09. \u518d\u4ee4F(x,y,z)=2x²+y²-z,\u5219\u66f2\u9762\u7684\u6cd5\u5411\u91cf=\uff08Fx,Fy,Fz)=(4x,2y,-1)=\uff08-1,-2,-1\uff09\uff0c\u89e3\u5f97\uff0cx=-1/4,y=-1\uff0c\u4e0b\u6765\u4f60
x²/a²+y²/b²+z²/c²=1，上点（x0,y0,z0）处的切平面方程为：
x0x/a²+y0y/b²+z0z/c²=1
推导过程：
令F(x,y,z)=x²/a²+y²/b²+z²/c²-1
Fx=2x/a²，Fy=2y/b²，Fz=2z/c²
n=(x0/a²，y0/b²，z0/c²)
切平面方程为
x0/a²(x-x0)+y0/b²(y-y0)+z0/c²(z-z0)=0
化简即得。
绛旓細杩欎釜鏄叕寮忥細x²/a²+y²/b²+z²/c²=1锛屼笂鐐癸紙x0,y0,z0锛夊鐨鍒囧钩闈㈡柟绋涓猴細x0x/a²+y0y/b²+z0z/c²=1 鎺ㄥ杩囩▼锛氫护F(x,y,z)=x²/a²+y²/b²+z²/c²-1 Fx=2x/a²锛孎y=2y/...
绛旓細璁鍒囧钩闈㈡柟绋涓簒+2y+z+D=0.鍒欏垏骞抽潰娉曞悜閲=锛1,2,1锛,鐢变簬娉曞悜閲忓彲姝ｅ彲璐燂紝鎵浠ュ垏骞抽潰娉曞悜閲忚繕绛変簬锛-1锛-2锛-1锛. 鍐嶄护F(x,y,z)=2x²+y²-z,鍒欐洸闈㈢殑娉曞悜閲=锛團x,Fy,Fz)=(4x,2y,-1)=锛-1,-2,-1锛夛紝瑙ｅ緱锛寈=-1/4,y=-1锛屼笅鏉ヤ綘 ...
绛旓細1. 鍒囧钩闈㈡柟绋鐨勪竴鑸舰寮忎负锛歕( F'_{x}(x_{0}, y_{0}, z_{0})(x - x_{0}) + F'_{y}(x_{0}, y_{0}, z_{0})(y - y_{0}) + F'_{z}(x_{0}, y_{0}, z_{0})(z - z_{0}) = 0 \)銆2. 娉曞钩闈㈡柟绋嬪彲浠ヨ〃绀轰负锛歕( 0(x - 1) + 1(y - 1)...
绛旓細1銆鍒囧钩闈㈡柟绋鏄疐'x(x0锛寉0锛寊0)(x-x0)+F'y(x0锛寉0锛寊0)(y-y0)+F'z(x0锛寉0锛寊0)(z-z0)=0銆2銆佹硶骞抽潰鏂圭▼鏄0(x-1)+1(y-1)+2(z-1)=0銆3銆佽繃绌洪棿鏇茬嚎鐨勫垏鐐癸紝涓斾笌鍒囩嚎鍨傜洿鐨勫钩闈紝绉颁负娉曞钩闈傚嵆鍨傜洿浜庤櫄鎷熸硶绾跨殑骞抽潰銆備緥濡傦紝鐞冧綋鐨勪腑蹇冧负绔偣鐨勫皠绾匡紝涓庣悆闈㈡墍鍦ㄧ殑姣涓...
绛旓細绗竴姝ワ紝鍏堝皢涓や釜鐐逛唬鍏鍒囧钩闈㈡柟绋锛屽緱鍒(1)(2)涓や釜鏂圭▼銆傜浜屾锛岀劧鍚庤繖涓や釜鏂圭▼鐩稿噺锛屽彲浠ュ緱鍑簒銆=y銆3銆楂樻暟鐨勫垏骞抽潰鏂圭▼鐨勭孩妗嗛噷闈㈡眰鍑虹殑绗笁姝ワ紝灏嗘棆杞姏鐗╅潰鍙妜銆=y銆備唬鍏(1)寮忥紝灏卞彲浠ユ眰鍑簒銆傚叿浣撶殑楂樻暟鐨勫垏骞抽潰鏂圭▼鐨勭孩妗嗛噷闈㈠緱鍑虹殑璇︾粏姝ラ鍙婅鏄庤涓娿
绛旓細f锛坸锛寉锛寊锛=x^2+y^2-z锛宖'x(x,y,z)=2x,f'y(x,y,z)=2y,f'z(x,y,z)=-1,鍥犱负涓庡钩闈㈠钩琛岋紝鎵浠=1锛寉=2锛寊=x^2+y^2=5,鍒囧钩闈㈡柟绋涓猴細2锛坸-1锛+4(y-2)-1脳锛坺-5)=2x+4y-z-5=0,
绛旓細y,z)锛滷(x-y+z,xy-yz+zx)姹傚亸瀵兼暟锛欸x锛滷u*1锛婩v*(y+z)锛孏y=Fu*(-1)锛婩v*(x-z)锛孏z=Fu*1锛婩v*(x-y)浠ｅ叆x=2锛寉=1锛寊=-1锛孎u=2锛孎v=-3锛屽緱Gx=2锛孏y=-11锛孏z=-1 鎵浠ュ垏骞抽潰鐨勬硶鍚戦噺鏄(2,-11,-1)锛鍒囧钩闈㈡柟绋鏄2(x-2)-11(y-1)-(z+1)=0锛岀瓟妗堟槸 D ...
绛旓細涓嶆槸浠绘剰鍙栧緱锛屾妸寮忓瓙鍖栫畝涓涓 璇︾粏杩囩▼濡傚浘鎵绀猴紝鏈変换浣曠枒鎯戯紝娆㈣繋杩介棶
绛旓細娉曠嚎鏂圭▼锛歺−x0Fx(x0,y0,z0)=y−y0Fy(x0,y0,z0)=z−z0Fz(x0,y0,z0).鍒囧钩闈㈡柟绋锛欶x(x0,y0,z0)(x−x0)+Fy(x0,y0,z0)(y−y0)+Fz(x0,y0,z0)(z−z0)=0.娉ㄨ锛 蹇冧腑濮嬬粓鎯崇潃涓涓壒渚嬶紝鐞冮潰锛歺2+y2+z2=R2.鐨悆鏀惧湪鍦颁笂锛屽湴闈㈠氨...
绛旓細姹傚嚭z瀵箈銆亂鐨勫亸瀵兼暟锛寊(x)=(-y/x^2)/(1+y^2/x^2)锛寊(y)=(1/x)/(1+y^2/x^2)锛屾妸鐐筂0鍧愭爣浠ｅ叆锛屽緱骞抽潰鐨勬硶鍚戦噺=锛坺(x)锛寊(y)锛-1锛=锛-1/2,1/2,-1锛夛紝鎵浠鍒囧钩闈㈡柟绋涓(-1/2)(x-1)+(1/2)(y-1)+(-1)(z-蟺/4)=0 ...
