F=(x^2/√a)+(y^2/√b)+(z^2/√c)-1
Fx=2x/√a
Fy=2y/√b
Fz=2z/√c
过点(x,y,z)的切平面方程：2x/√a(X-x)+2y/√b(Y-y)+2z/√c(Z-z)=0
令Y=Z=0代入：.x/√a(X-x)+y/√b(-y)+z/√c(-z)=0
x/√a(X-x)=y^2/√b+z^/√c=1-(x^2/√a) X=√a/x
该平面与坐标轴轴的截距√a/x,√b/y,√c/z
体积=(1/6)√abc/xyz
先求(1/6)√abc/xyz在条件(x^2/√a)+(y^2/√b)+(z^2/√c)=1下的极值
F=(1/6)√abc/xyz+λ[(x^2/√a)+(y^2/√b)+(z^2/√c)-1]
Fx=-(1/6)√abc/x^2yz+2λx/√a=0
Fy=-(1/6)√abc/xy^2z+2λy/√b=0
Fy=-(1/6)√abc/xyz^2+2λz/√c=0
(x^2/√a)+(y^2/√b)+(z^2/√c)=1
求得：√a/x^2=√b/y^2=√c/y^2=3
解得：x=√(√a/3) y=√(√b/3) z=√(√c/3)