Answer
$2x+4y-z=4$
and
$\frac{x-1}{2}=\frac{y-1}{4}=\frac{z-2}{-1}=t$
or
$x=1+2t$, $y=1+4t$, $z=2-t$
See the attached graphs 1 and 2.
Work Step by Step
Given:$z=x^2+y^4$
Equation for a tangent plane is given as:
$z-2=2(x-1)+4(y-1)$
$z-2=2x-2+4y-4$
$z=2x+4y-4$
$2x+4y-z=4$
Equation of normal line is:
$\frac{x-1}{2}=\frac{y-1}{4}=\frac{z-2}{-1}=t$
or
$x=1+2t$, $y=1+4t$, $z=2-t$
See the attached graphs 1 and 2.
