求椭球面x²+2y+z²=1上平行于平面x-y+2z=0的切平面方程,
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![求椭球面x²+2y+z²=1上平行于平面x-y+2z=0的切平面方程,](/uploads/image/z/7996954-58-4.jpg?t=%E6%B1%82%E6%A4%AD%E7%90%83%E9%9D%A2x%26%23178%3B%2B2y%2Bz%26%23178%3B%3D1%E4%B8%8A%E5%B9%B3%E8%A1%8C%E4%BA%8E%E5%B9%B3%E9%9D%A2x-y%2B2z%3D0%E7%9A%84%E5%88%87%E5%B9%B3%E9%9D%A2%E6%96%B9%E7%A8%8B%2C)
求椭球面x²+2y+z²=1上平行于平面x-y+2z=0的切平面方程,
求椭球面x²+2y+z²=1上平行于平面x-y+2z=0的切平面方程,
求椭球面x²+2y+z²=1上平行于平面x-y+2z=0的切平面方程,
x²+2y+z²=1
F(x,y,z)=x²+2y+z²-1
Fx=2x
Fy=2
Fz=2z
设切点为(x0,y0,z0)
则
2x0/1=2/(-1)=2z0/2
所以
x0=-1
z0=-2
又x0²+2y0+z0²=1
1+2y0+4=1
y0=-2
所以
切点为(-1,-2,-2)
切平面为:
x+1-(y+2)+2(z+2)=0
x-y+2z+3=0