@高数大神，为什么椭球面的切平面是它？求解释 大学高数下的一道椭球面的题目，急！！！！！！！高手进！！！
\u9ad8\u6570\uff0c\u692d\u7403\u9762\u4e00\u70b9\u7684\u5207\u5e73\u9762\u95ee\u9898\uff1f\u9996\u5148\uff0c\u5982\u679c\u67d0\u5e73\u9762\u5782\u76f4xoy.\u90a3\u4e48\u8be5\u5e73\u9762\u5fc5\u5b9a\u4e0d\u542b\u6709\u5411\u91cfz\uff0c\u4e5f\u5c31\u662f\u5e73\u9762\u7684\u6cd5\u5411\u91cf\u5173\u4e8ez\u65b9\u5411\u90e8\u5206\u4e3a0.
\u56e0\u4e3a\u6cd5\u5411\u91cfn\u7684z\u90e8\u5206\u662f2y-z,\u5219
\u53ef\u77e52y-z=0.\u5373z=2y
F=(x^2/\u221aa)+(y^2/\u221ab)+(z^2/\u221ac)-1
Fx=2x/\u221aa
Fy=2y/\u221ab
Fz=2z/\u221ac
\u8fc7\u70b9(x,y,z)\u7684\u5207\u5e73\u9762\u65b9\u7a0b\uff1a2x/\u221aa(X-x)+2y/\u221ab(Y-y)+2z/\u221ac(Z-z)=0
\u4ee4Y=Z=0\u4ee3\u5165\uff1a. x/\u221aa(X-x)+y/\u221ab(-y)+z/\u221ac(-z)=0
x/\u221aa(X-x)=y^2/\u221ab+z^/\u221ac=1-(x^2/\u221aa) X=\u221aa/x
\u8be5\u5e73\u9762\u4e0e\u5750\u6807\u8f74\u8f74\u7684\u622a\u8ddd\u221aa/x\uff0c\u221ab/y, \u221ac/z
\u4f53\u79ef=(1/6)\u221aabc/xyz
\u5148\u6c42(1/6)\u221aabc/xyz\u5728\u6761\u4ef6(x^2/\u221aa)+(y^2/\u221ab)+(z^2/\u221ac)=1\u4e0b\u7684\u6781\u503c
F=(1/6)\u221aabc/xyz+\u03bb[(x^2/\u221aa)+(y^2/\u221ab)+(z^2/\u221ac)-1]
Fx=-(1/6)\u221aabc/x^2yz+2\u03bbx/\u221aa=0
Fy=-(1/6)\u221aabc/xy^2z+2\u03bby/\u221ab=0
Fy=-(1/6)\u221aabc/xyz^2+2\u03bbz/\u221ac=0
(x^2/\u221aa)+(y^2/\u221ab)+(z^2/\u221ac)=1
\u6c42\u5f97\uff1a\u221aa/x^2=\u221ab/y^2=\u221ac/y^2=3
\u89e3\u5f97\uff1ax=\u221a(\u221aa/3) y=\u221a(\u221ab/3) z=\u221a(\u221ac/3)
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。
还是求问这是哪本书啊
1.pai这个点在椭球面上，正方向，XYZ都是正的
你好，我正在考研，能告诉我你这道题是哪本书上的吗？这个对我很重要，非常感谢
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