Answer
$8x+2y-z=5$
Work Step by Step
As we are given that $4x^2+y^2-z=0$
Since, we have the vector equation $r(x,y,z)=r_0+t \nabla f(r_0)$
The equation of the tangent line for $\nabla f(1,1,5)=\lt 8,2,-1 \gt$ is
$8(x-1)+2(y-1)-1(z-5)=0$
or, $8x+2y-z=5$
