Answer
$8x+2y-z=5$
Work Step by Step
The vector equation is given by: $r(x,y,z)=r_0+t \nabla f(r_0)$
Given: $4x^2+y^2-z=0$
The equation of tangent line for $\nabla f(1,1,5)=\lt 8,2,-1 \gt$ is given as follows:
Now, $(8)(x-1)+(2)(y-1)-(1)(z-5)=0$
or, $8x-8+2y-2-z+5=0$
Thus, $8x+2y-z=5$
