二次曲面方程及其图形 求二次曲面过在点处的切平面及法线方程,谢谢
\u4e8c\u6b21\u66f2\u9762\u65b9\u7a0b\u5206\u7c7b\u7684\u65b9\u6cd5\u6709\u51e0\u79cd\u5e38\u89c1\u7684\u5927\u6982\u6709
1\u3001\u67f1\u9762\uff1aF\uff08x,y\uff09=0\uff08z\u662f\u5168\u4f53\u5b9e\u6570\uff09\u4f8b\u5982x^2+y^2=R^2\u5706\u67f1\u66f2\u9762
2\u3001\u5706\u67f1\u66f2\u9762\uff1a\u65b9\u7a0b\u662f2\u6b21\u5176\u6b21\u5f0fF\uff08x^2,y^2,z^2\uff09=0\u4f8b\u5982\uff1ax^2/4+y^2/8=z^2\uff08\u5305\u62ec\u692d\u7403\u9762\uff09
3\u3001\u65cb\u8f6c\u66f2\u9762\uff1af\uff08\u6b63\u8d1f\u6839\u4e0b\uff08x^2+y^2\uff09,z\uff09=0\u6bd4\u5982\uff1a\u6839\u4e0bx^2+y^2=|y1|,z=z1
4\u3001\u4e8c\u6b21\u66f2\u9762\u4e00\u822c\u5f0f\uff1aAx+By+Cz+Dxy+Eyx+Fzx+Gx+Hy+Iz+J=0
1\u3001\u4e8c\u6b21\u66f2\u9762\u8fc7\u5728\u70b9\u5904\u7684\u5207\u5e73\u9762\u53ca\u6cd5\u7ebf\u65b9\u7a0b\u5982\u4e0b\uff1a
f(x\uff0cy\uff0cz) = x^2+2y^2+3z^2-36\uff0c
\u5219 fx ' = 2x = 2\uff0c
fy ' = 4y = 8\uff0c
fz ' = 6z = 18\uff0c
\u5207\u5e73\u9762\u65b9\u7a0b\u4e3a 2(x-1)+8(y-2)+18(z-3) = 0\uff0c
\u6cd5\u7ebf\u65b9\u7a0b\u4e3a (x-1)/2 = (y-2)/8 = (z-3)/18 \u3002
2\u3001\u5207\u5e73\u9762\u53ca\u6cd5\u7ebf\u65b9\u7a0b\u8ba1\u7b97\u65b9\u6cd5\uff1a
\u5bf9\u4e8e\u50cf\u4e09\u89d2\u5f62\u8fd9\u6837\u7684\u591a\u8fb9\u5f62\u6765\u8bf4\uff0c\u591a\u8fb9\u5f62\u4e24\u6761\u76f8\u4e92\u4e0d\u5e73\u884c\u7684\u8fb9\u7684\u53c9\u79ef\u5c31\u662f\u591a\u8fb9\u5f62\u7684\u6cd5\u7ebf\u3002
\u7528\u65b9\u7a0b ax + by + cz = d \u8868\u793a\u7684\u5e73\u9762\uff0c\u5411\u91cf (a,b,c) \u5c31\u662f\u8be5\u5e73\u9762\u7684\u6cd5\u5411\u91cf\u3002
S \u662f\u66f2\u7ebf\u5750\u6807 x(s, t) \u8868\u793a\u7684\u66f2\u9762\uff0c\u5176\u4e2d s \u53ca t \u662f\u5b9e\u6570\u53d8\u91cf\uff0c\u90a3\u4e48\u7528\u504f\u5bfc\u6570\u53c9\u79ef\u8868\u793a\u7684\u6cd5\u7ebf\u4e3a\u3002
\u66f2\u9762 S \u7528\u9690\u51fd\u6570\u8868\u793a\uff0c\u70b9\u96c6\u5408 (x,y,z) \u6ee1\u8db3 F(x,y,z) = 0\uff0c\u90a3\u4e48\u5728\u70b9 (x,y,z) \u5904\u7684\u66f2\u9762\u6cd5\u7ebf\u7528\u68af\u5ea6\u8868\u793a\u4e3a\u3002
\u6269\u5c55\u8d44\u6599\uff1a
1\u3001\u4e8c\u6b21\u66f2\u9762\u8fc7\u5728\u70b9\u5904\u7684\u5207\u5e73\u9762\u53ca\u6cd5\u7ebf\u65b9\u7a0b\u4f8b\u9898\u89e3\u91ca
zx=2x\uff1bzy=6y
\u6240\u4ee5,(1,1,3)\u5904\u7684\u6cd5\u5411\u91cf\u4e3a\uff1a(zx,zy,-1)=(2,4,-1)\uff1b
\u5207\u5e73\u9762\u65b9\u7a0b\u4e3a\uff1a2(x-1)+4(x-1)-(x-3)=0\uff1b
\u5373\u4e3a\uff1a2x+4y-z-3=0\uff1b
\u6cd5\u7ebf\u65b9\u7a0b\u4e3a\uff1a(x-1)/2=(y-1)/4=(z-3)/(-1)\uff1b
2\u3001\u5207\u5e73\u9762\u53ca\u6cd5\u7ebf\u65b9\u7a0b\u8ba1\u7b97\u6e29\u99a8\u63d0\u793a
\u5982\u679c\u66f2\u9762\u5728\u67d0\u70b9\u6ca1\u6709\u5207\u5e73\u9762\uff0c\u90a3\u4e48\u5728\u8be5\u70b9\u5c31\u6ca1\u6709\u6cd5\u7ebf\u3002
\u4f8b\u5982\uff0c\u5706\u9525\u7684\u9876\u70b9\u4ee5\u53ca\u5e95\u9762\u7684\u8fb9\u7ebf\u5904\u90fd\u6ca1\u6709\u6cd5\u7ebf\uff0c\u4f46\u662f\u5706\u9525\u7684\u6cd5\u7ebf\u662f\u51e0\u4e4e\u5904\u5904\u5b58\u5728\u7684\u3002\u901a\u5e38\u4e00\u4e2a\u6ee1\u8db3Lipschitz\u8fde\u7eed\u7684\u66f2\u9762\u53ef\u4ee5\u8ba4\u4e3a\u6cd5\u7ebf\u51e0\u4e4e\u5904\u5904\u5b58\u5728\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u6cd5\u7ebf
2.这个问题答案,你可以通过我第一个题的解答去想.很容易就写出来了,
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