Question

помогите кто нибудь решить задачу.

Answer 1

$(x-1)^2+(y+2)^2+(z-2)^2=27; ;; ; M_0(2;-1;-3)\\f(x,y,z)=(x-1)^2+(y+2)^2+(z-2)^2-27\\f'_{x}(M_0)(x-x_0)+f'_{y}(M_0)(y-y_0)+f'_{z}(M_0)(z-z_0)=0\\f'_{x}(M_0)=2(x-1)|_{x_0=2}=2(2-1)=2\\f'_{y}(M_0)=2(y+2)|_{y_0=-1}=2(-1+2)=2\\f'_{z}(M_0)=2(z-2)|_{z_0=-3}=2cdot (-3-3)=-10\\2(x-2)+2(y+1)-10(z+3)=0\\2x+2y-10z-32=0$